study guide and intervention name study guide and intervention
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Name ________________________________________ Hour ________
Midpoint Worksheet& Distance Day 2
Name ______________________________________ Hour ________
1-3 Midpoint Formula Day 2Worksheet
MIDPOINT
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
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of T
he M
cGra
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NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PMLe
sson
1-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
Find the coordinates of the missing endpoint if P is the midpoint of NQ.
15. 16. 17.
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 20 Glencoe Geometry
Skills PracticeDistance and Midpoints
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Find the distance between each pair of points.
5.
x
y
O
F
G
6.
x
y
O
D
S
7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)
9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)
11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. −−− DE 14. −−− BC
15. −−− BD 16. −−− AD
Find the coordinates of the midpoint of a segment with the given endpoints.
17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)
Find the coordinates of the missing endpoint if P is the midpoint of −−−
NQ .
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
–6 –4 –2 0 2 4 6 8 10
J K L M N
1-3
001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 20 Glencoe Geometry
Skills PracticeDistance and Midpoints
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Find the distance between each pair of points.
5.
x
y
O
F
G
6.
x
y
O
D
S
7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)
9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)
11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. −−− DE 14. −−− BC
15. −−− BD 16. −−− AD
Find the coordinates of the midpoint of a segment with the given endpoints.
17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)
Find the coordinates of the missing endpoint if P is the midpoint of −−−
NQ .
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
–6 –4 –2 0 2 4 6 8 10
J K L M N
1-3
001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 20 Glencoe Geometry
Skills PracticeDistance and Midpoints
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Find the distance between each pair of points.
5.
x
y
O
F
G
6.
x
y
O
D
S
7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)
9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)
11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. −−− DE 14. −−− BC
15. −−− BD 16. −−− AD
Find the coordinates of the midpoint of a segment with the given endpoints.
17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)
Find the coordinates of the missing endpoint if P is the midpoint of −−−
NQ .
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
–6 –4 –2 0 2 4 6 8 10
J K L M N
1-3
001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM
Find the coordinates of the missing endpoint if E is the midpoint of DF.
18. 19. 20.
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on 1
-3
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yrig
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ncoe
/McG
raw
-Hill
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he M
cGra
w-H
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ompa
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, Inc
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NAME DATE PERIOD
PDF Pass
Chapter 1 21 Glencoe Geometry
PracticeDistance and Midpoints
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Find the distance between each pair of points.
5.
x
y
OM
Z 6.
x
y
O
E
S
7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)
Use the number line to find the coordinate of the midpoint of each segment.
11. −− RT 12. −−− QR
13. −− ST 14. −− PR
Find the coordinates of the midpoint of a segment with the given endpoints.
15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)
Find the coordinates of the missing endpoint if E is the midpoint of −− DF .
17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)
20. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
1-3
001_024_GEOCRMC01_890510.indd 21001_024_GEOCRMC01_890510.indd 21 5/23/08 5:04:40 PM5/23/08 5:04:40 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 21 Glencoe Geometry
PracticeDistance and Midpoints
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Find the distance between each pair of points.
5.
x
y
OM
Z 6.
x
y
O
E
S
7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)
Use the number line to find the coordinate of the midpoint of each segment.
11. −− RT 12. −−− QR
13. −− ST 14. −− PR
Find the coordinates of the midpoint of a segment with the given endpoints.
15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)
Find the coordinates of the missing endpoint if E is the midpoint of −− DF .
17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)
20. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
1-3
001_024_GEOCRMC01_890510.indd 21001_024_GEOCRMC01_890510.indd 21 5/23/08 5:04:40 PM5/23/08 5:04:40 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 21 Glencoe Geometry
PracticeDistance and Midpoints
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Find the distance between each pair of points.
5.
x
y
OM
Z 6.
x
y
O
E
S
7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)
Use the number line to find the coordinate of the midpoint of each segment.
11. −− RT 12. −−− QR
13. −− ST 14. −− PR
Find the coordinates of the midpoint of a segment with the given endpoints.
15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)
Find the coordinates of the missing endpoint if E is the midpoint of −− DF .
17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)
20. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
1-3
001_024_GEOCRMC01_890510.indd 21001_024_GEOCRMC01_890510.indd 21 5/23/08 5:04:40 PM5/23/08 5:04:40 PM
Name ______________________________________ Hour ________
1-3 Midpoint Formula Day 2Worksheet
MIDPOINT
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
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on 1
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Chapter 1 19 Glencoe Geometry
Study Guide and Intervention (continued)
Distance and Midpoints
–10 –8 –6 –4 –2 0 2 4 6 8
A B C D E F G
-3 -2 -1 0 1 2
P Q
1-3
Midpoint of a Segment
Midpoint on a Number Line
If the coordinates of the endpoints of a segment are x1 and x2,
then the coordinate of the midpoint of the segment is x1 + x2 −
2 .
Midpoint on a Coordinate Plane
If a segment has endpoints with coordinates (x1, y1) and (x2, y2),
then the coordinates of the midpoint of the segment are ( x1 + x2 −
2 ,
y1 + y2 − 2 ) .
Find the coordinate of the midpoint of −−
PQ .
The coordinates of P and Q are -3 and 1.
If M is the midpoint of −−−
PQ , then the coordinate of M is -3 + 1 − 2 = -2 −
2 or -1.
Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).
M = ( x1+ x2 −
2 ,
y1+ y2 − 2 ) = ( -2 + 4 −
2 , 4 + 1 −
2 ) or (1, 2.5)
ExercisesUse the number line to find the coordinate of the midpoint of each segment.
1. −−− CE 2. −−− DG
3. −− AF 4. −−− EG
5. −− AB 6. −−− BG
7. −−− BD 8. −−− DE
Find the coordinates of the midpoint of a segment with the given endpoints.
9. A(0, 0), B(12, 8) 10. R(-12, 8), S(6, 12)
11. M(11, -2), N(-9, 13) 12. E(-2, 6), F(-9, 3)
13. S(10, -22), T(9, 10) 14. K(-11, 2), L(-19, 6)
Example 1
Example 2
001_024_GEOCRMC01_890510.indd 19001_024_GEOCRMC01_890510.indd 19 5/23/08 5:04:29 PM5/23/08 5:04:29 PM
Find the coordinates of the missing endpoint if P is the midpoint of NQ.
15. 16. 17.
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-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 20 Glencoe Geometry
Skills PracticeDistance and Midpoints
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Find the distance between each pair of points.
5.
x
y
O
F
G
6.
x
y
O
D
S
7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)
9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)
11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. −−− DE 14. −−− BC
15. −−− BD 16. −−− AD
Find the coordinates of the midpoint of a segment with the given endpoints.
17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)
Find the coordinates of the missing endpoint if P is the midpoint of −−−
NQ .
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
–6 –4 –2 0 2 4 6 8 10
J K L M N
1-3
001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 20 Glencoe Geometry
Skills PracticeDistance and Midpoints
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Find the distance between each pair of points.
5.
x
y
O
F
G
6.
x
y
O
D
S
7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)
9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)
11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. −−− DE 14. −−− BC
15. −−− BD 16. −−− AD
Find the coordinates of the midpoint of a segment with the given endpoints.
17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)
Find the coordinates of the missing endpoint if P is the midpoint of −−−
NQ .
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
–6 –4 –2 0 2 4 6 8 10
J K L M N
1-3
001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 20 Glencoe Geometry
Skills PracticeDistance and Midpoints
Use the number line to find each measure.
1. LN 2. JL
3. KN 4. MN
Find the distance between each pair of points.
5.
x
y
O
F
G
6.
x
y
O
D
S
7. K(2, 3), F(4, 4) 8. C(-3, -1), Q(-2, 3)
9. Y(2, 0), P(2, 6) 10. W(-2, 2), R(5, 2)
11. A(-7, -3), B(5, 2) 12. C(-3, 1), Q(2, 6)
Use the number line to find the coordinate of the midpoint of each segment.
13. −−− DE 14. −−− BC
15. −−− BD 16. −−− AD
Find the coordinates of the midpoint of a segment with the given endpoints.
17. T(3, 1), U(5, 3) 18. J(-4, 2), F(5, -2)
Find the coordinates of the missing endpoint if P is the midpoint of −−−
NQ .
19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(-1, 5)
–6 –4 –2 0 2 4 6 8 10 12
A B C D E
–6 –4 –2 0 2 4 6 8 10
J K L M N
1-3
001_024_GEOCRMC01_890510.indd 20001_024_GEOCRMC01_890510.indd 20 5/23/08 5:04:34 PM5/23/08 5:04:34 PM
Find the coordinates of the missing endpoint if E is the midpoint of DF.
18. 19. 20.
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on 1
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ncoe
/McG
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-Hill
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NAME DATE PERIOD
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Chapter 1 21 Glencoe Geometry
PracticeDistance and Midpoints
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Find the distance between each pair of points.
5.
x
y
OM
Z 6.
x
y
O
E
S
7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)
Use the number line to find the coordinate of the midpoint of each segment.
11. −− RT 12. −−− QR
13. −− ST 14. −− PR
Find the coordinates of the midpoint of a segment with the given endpoints.
15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)
Find the coordinates of the missing endpoint if E is the midpoint of −− DF .
17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)
20. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
1-3
001_024_GEOCRMC01_890510.indd 21001_024_GEOCRMC01_890510.indd 21 5/23/08 5:04:40 PM5/23/08 5:04:40 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 21 Glencoe Geometry
PracticeDistance and Midpoints
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Find the distance between each pair of points.
5.
x
y
OM
Z 6.
x
y
O
E
S
7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)
Use the number line to find the coordinate of the midpoint of each segment.
11. −− RT 12. −−− QR
13. −− ST 14. −− PR
Find the coordinates of the midpoint of a segment with the given endpoints.
15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)
Find the coordinates of the missing endpoint if E is the midpoint of −− DF .
17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)
20. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
1-3
001_024_GEOCRMC01_890510.indd 21001_024_GEOCRMC01_890510.indd 21 5/23/08 5:04:40 PM5/23/08 5:04:40 PM
Less
on 1
-3
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a d
ivis
ion
of T
he M
cGra
w-H
ill C
ompa
nies
, Inc
.
NAME DATE PERIOD
PDF Pass
Chapter 1 21 Glencoe Geometry
PracticeDistance and Midpoints
Use the number line to find each measure.
1. VW 2. TV
3. ST 4. SV
Find the distance between each pair of points.
5.
x
y
OM
Z 6.
x
y
O
E
S
7. L(-7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)
9. V(-2, 5), M(0, -4) 10. C(-2, -1), K(8, 3)
Use the number line to find the coordinate of the midpoint of each segment.
11. −− RT 12. −−− QR
13. −− ST 14. −− PR
Find the coordinates of the midpoint of a segment with the given endpoints.
15. K(-9, 3), H(5, 7) 16. W(-12, -7), T(-8, -4)
Find the coordinates of the missing endpoint if E is the midpoint of −− DF .
17. F(5, 8), E(4, 3) 18. F(2, 9), E(-1, 6) 19. D(-3, -8), E(1, -2)
20. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.
–6 –4–10 –8 –2 0 2 4 6
P Q R S T
–6 –4–10 –8 –2 0 2 4 6 8
S T U V W
1-3
001_024_GEOCRMC01_890510.indd 21001_024_GEOCRMC01_890510.indd 21 5/23/08 5:04:40 PM5/23/08 5:04:40 PM
DISTANCE PROBLEM REVIEW
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cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 18 Glencoe Geometry
Study Guide and InterventionDistance and Midpoints
Distance Between Two Points
Distance on a Number Line Distance in the Coordinate Plane
A B
x1 x2
AB = |x1 - x2| or |x2 - x1|
Distance Formula: y
x
B(x2, y2)
A(x1, y1)
d = √ """"""""" (x2 - x1)2 + (y2 - y1)
2
Use the number line to find AB.
AB = |(-4) - 2| = |- 6| = 6
-5 -4 -3 -2 -1 0 1 2 3
A B
Find the distance between A(-2, -1) and B(1, 3).Distance Formula
d = √ """"""""" (x2 - x1)2 + ( y2 - y1)
2
AB = √ """""""""" (1 - (-2))2+ (3 - (-1))2
AB = √ """" (3)2 + (4)2
= √ "" 25 = 5
ExercisesUse the number line to find each measure.
1. BD 2. DG
3. AF 4. EF
5. BG 6. AG
7. BE 8. DE
Find the distance between each pair of points.
9. A(0, 0), B(6, 8) 10. R(-2, 3), S(3, 15)
11. M(1, -2), N(9, 13) 12. E(-12, 2), F(-9, 6)
13. X(0, 0), Y(15, 20) 14. O(-12, 0), P(-8, 3)
15. C(11, -12), D(6, 2) 16. K(-2, 10), L(-4, 3)
-10 -8 -6 -4 -2 0 2 4 6 8
A B C D E F G
1-3
Example 1 Example 2
001_024_GEOCRMC01_890510.indd 18001_024_GEOCRMC01_890510.indd 18 5/23/08 5:04:12 PM5/23/08 5:04:12 PM
Find the distance between each pair of points.21. L(-7, 0), Y(5, 9) 22. U(1, 3), B(4, 6) 23. V(-2, 5), M(0, -4)
WORD PROBLEMS1. 2.
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-Hill C
ompanies, Inc.
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Chapter 1 22 Glencoe Geometry
Word Problem PracticeDistance and Midpoints
1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?
y
xO
Cabins
Mess Hall
2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?
3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?
y
xO
4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.
5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.
y
xO
Ben’s House
Kate’s House
a. How many yards apart are Kate’s and Ben’s homes?
b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.
1-3
001_024_GEOCRMC01_890510.indd 22001_024_GEOCRMC01_890510.indd 22 5/23/08 5:04:50 PM5/23/08 5:04:50 PM
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cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 22 Glencoe Geometry
Word Problem PracticeDistance and Midpoints
1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?
y
xO
Cabins
Mess Hall
2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?
3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?
y
xO
4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.
5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.
y
xO
Ben’s House
Kate’s House
a. How many yards apart are Kate’s and Ben’s homes?
b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.
1-3
001_024_GEOCRMC01_890510.indd 22001_024_GEOCRMC01_890510.indd 22 5/23/08 5:04:50 PM5/23/08 5:04:50 PM
3.
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cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 22 Glencoe Geometry
Word Problem PracticeDistance and Midpoints
1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?
y
xO
Cabins
Mess Hall
2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?
3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?
y
xO
4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.
5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.
y
xO
Ben’s House
Kate’s House
a. How many yards apart are Kate’s and Ben’s homes?
b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.
1-3
001_024_GEOCRMC01_890510.indd 22001_024_GEOCRMC01_890510.indd 22 5/23/08 5:04:50 PM5/23/08 5:04:50 PM
DISTANCE PROBLEM REVIEW
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 18 Glencoe Geometry
Study Guide and InterventionDistance and Midpoints
Distance Between Two Points
Distance on a Number Line Distance in the Coordinate Plane
A B
x1 x2
AB = |x1 - x2| or |x2 - x1|
Distance Formula: y
x
B(x2, y2)
A(x1, y1)
d = √ """"""""" (x2 - x1)2 + (y2 - y1)
2
Use the number line to find AB.
AB = |(-4) - 2| = |- 6| = 6
-5 -4 -3 -2 -1 0 1 2 3
A B
Find the distance between A(-2, -1) and B(1, 3).Distance Formula
d = √ """"""""" (x2 - x1)2 + ( y2 - y1)
2
AB = √ """""""""" (1 - (-2))2+ (3 - (-1))2
AB = √ """" (3)2 + (4)2
= √ "" 25 = 5
ExercisesUse the number line to find each measure.
1. BD 2. DG
3. AF 4. EF
5. BG 6. AG
7. BE 8. DE
Find the distance between each pair of points.
9. A(0, 0), B(6, 8) 10. R(-2, 3), S(3, 15)
11. M(1, -2), N(9, 13) 12. E(-12, 2), F(-9, 6)
13. X(0, 0), Y(15, 20) 14. O(-12, 0), P(-8, 3)
15. C(11, -12), D(6, 2) 16. K(-2, 10), L(-4, 3)
-10 -8 -6 -4 -2 0 2 4 6 8
A B C D E F G
1-3
Example 1 Example 2
001_024_GEOCRMC01_890510.indd 18001_024_GEOCRMC01_890510.indd 18 5/23/08 5:04:12 PM5/23/08 5:04:12 PM
Find the distance between each pair of points.21. L(-7, 0), Y(5, 9) 22. U(1, 3), B(4, 6) 23. V(-2, 5), M(0, -4)
WORD PROBLEMS1. 2.
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 22 Glencoe Geometry
Word Problem PracticeDistance and Midpoints
1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?
y
xO
Cabins
Mess Hall
2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?
3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?
y
xO
4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.
5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.
y
xO
Ben’s House
Kate’s House
a. How many yards apart are Kate’s and Ben’s homes?
b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.
1-3
001_024_GEOCRMC01_890510.indd 22001_024_GEOCRMC01_890510.indd 22 5/23/08 5:04:50 PM5/23/08 5:04:50 PM
Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 22 Glencoe Geometry
Word Problem PracticeDistance and Midpoints
1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?
y
xO
Cabins
Mess Hall
2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?
3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?
y
xO
4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.
5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.
y
xO
Ben’s House
Kate’s House
a. How many yards apart are Kate’s and Ben’s homes?
b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.
1-3
001_024_GEOCRMC01_890510.indd 22001_024_GEOCRMC01_890510.indd 22 5/23/08 5:04:50 PM5/23/08 5:04:50 PM
3.
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Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
PDF Pass
Chapter 1 22 Glencoe Geometry
Word Problem PracticeDistance and Midpoints
1. CAMPGROUND Troop 175 is designing their new campground by first mapping everything on a coordinate grid. They have found a location for the mess hall and for their cabins. They want the bathrooms to be halfway between these two. What will be the coordinates of the location of the bathrooms?
y
xO
Cabins
Mess Hall
2. PIZZA Calvin’s home is located at the midpoint between Fast Pizza and Pizza Now. Fast Pizza is a quarter mile away from Calvin’s home. How far away is Pizza Now from Calvin’s home? How far apart are the two pizzerias?
3. SPIRALS Caroline traces out the spiral shown in the figure. The spiral begins at the origin. What is the shortest distance between Caroline’s starting point and her ending point?
y
xO
4. WASHINGTON, D.C. The United States Capitol is located 800 meters south and 2300 meters to the east of the White House. If the locations were placed on a coordinate grid, the White House would be at the origin. What is the distance between the Capitol and the White House? Round your answer to the nearest meter.
5. MAPPING Ben and Kate are making a map of their neighborhood on a piece of graph paper. They decide to make one unit on the graph paper correspond to 100 yards. First, they put their homes on the map as shown below.
y
xO
Ben’s House
Kate’s House
a. How many yards apart are Kate’s and Ben’s homes?
b. Their friend Jason lives exactly halfway between Ben and Kate. Mark the location of Jason’s home on the map.
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