Chapter 1.3-1.4

Midpoint FormulaConstruct Midpoints

• Midpoint (of a segment) – the point that splits the segment into 2 equal parts (where the segment is cut)

• If X is the midpoint of AC and XC = 10, how long is AX? AC?

A Z B

With AlgebraZ is midpoint of MP. Find x.

M Z P

3x 24 - x

3x = 24 – x

+1x= + 1x

4x = 24

X = 6

Bisector (of a segment) – a line, segment ray, or plane that intersects a segment at the midpoint (it does the cutting)

A Z B

mbisector

midpoint

Hatch Marks – short slash markings that show two or more segments are equal in length

W X Y Z

WX = YZ

Congruent - segments that have the same measure (like equal)

~

Urkle Stephon

Zack Cody

2 1midpoint2

x xx

2 1

midpoint2

y yy

midpoint midpoint( , )x y

Midpoint formula:

2 1midpoint2

x xx

2 1midpoint2

y yy

midpoint midpoint( , )x y

Find the midpoint whose endpoints are (2, -3) and (-14, 13)1, 1( )x y 2, 2( )x y

14 2

212

6

( , )6

13 3

210

5

5

+

2= y midpoint

+

2= x midpoint

2 1midpoint2

x xx

2 1midpoint2

y yy

midpoint midpoint( , )x y

Find the midpoint whose endpoints are (1, -2) and (-17, 16)1, 1( )x y 2, 2( )x y

17 1

216

8

( , )8

16 2

214

7

7

+

2= x midpoint

+

2= y midpoint

What if you are missing an endpoint ?

• When given the midpoint and one endpoint, set up the formula just as before.

(-2,2) (-3,-5)

( ?, ?)

M(-3, -5) is the midpoint of RS. If S has a coordinates

(-2, 2), find the coordinates of R.

2, 2( )x y

2

12 x 6

( , )4

2 1y

12

,( )m mx y

(x1, y1) (-2, 2)M(-3, -5)

3 5(2) (2)

2 2

1x 4

(2) (2)

12 y 102 2

1y 12

R S

+

2= +

2=

(x1, y1)

x1 y1

M(4, 2) is the midpoint of RS. If S has a coordinates (5, -2), find the coordinates of R.

2, 2( )x y

5

15 x 8

( , )3

2

6

,( )m mx y

R (x1, y1) S (5,-2)M(4, 2)

4 2(2) (2)

5 5

1x 3

(2) (2)

12 y 42 2

1y 6

+

2= +

2=

x1 y1

(x1, y1)

Book p.41-44

The End!