LESSON
146 Domain 4: Geometry
Dup
licat
ing
any
part
of t
his
book
is p
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EXAMPLE A LinesegmentCDisplottedonthecoordinateplane .Whatisthelengthof
___CD ?
Identifythecoordinatesofeachendpoint .
PointCisat(4,3) .PointDisat(10,11) .
ApplythePythagoreantheorem .
a21b25c2
621825c2
361645c2
1005c2
105c
▸Thelengthof___
CD is10units .
3
1Howcanyoufindthelengthofthelinesegment?
Thelinesegmentisnothorizontalorvertical,sofindingthelengthisnotassimpleascountingunitsorsubtractingcoordinates .However,linesegmentCDcanbecomethehypotenuseofarighttriangle,withonehorizontallegandoneverticalleg,asshown .
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Nowyoucancountunitsorsubtractcoordinatestofindthelengthsofthelegs .
Thehorizontallegconnects(4,3)to(10,3),sosubtractthex-coordinates .
Itslengthis102456units .
Theverticallegconnects(10,3)to(10,11),sosubtractthey-coordinates .
Itslengthis112358units .
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Applying the Pythagorean Theoremon the Coordinate Plane27
Showanotherwaytodrawtherighttriangleforthisproblem .
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MODEl
Lesson 27: Applying the Pythagorean Theorem on the Coordinate Plane 147
Dup
licat
ing
any
part
of t
his
book
is p
rohi
bite
d by
law
.
EXAMPLE B WhatisthedistancebetweenpointsRandS?
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S
R
Howcanyoufindthelengthofthelinesegment?
ConnectpointsRandStoformthehypotenuseofarighttriangle .
Thendrawhorizontalandverticallegs,asshown .
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1ApplythePythagoreantheorem .
a21b25c2
5211225c2
2511445c2
1695c2
135c
▸ThedistancebetweenpointsRandSis13units .
2
WhatisthedistancebetweenpointsTandV?Estimateyouranswertothenearesttenth .
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Practice
148 Domain 4: Geometry
Dup
licat
ing
any
part
of t
his
book
is p
rohi
bite
d by
law
.
Determine the length of a line segment with the given endpoints. Use Math Tool: Coordinate Plane.
1. (0,7)and(0,1) 2. (4,8)and(6,8)
Be sure to subtract the lesser coordinate from the greater coordinate.
HINT
3. (21,12)and(21,7)
Determine the length of each line segment. Show your work.
4.
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B
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6.
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7.
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K
L
Lesson 27: Applying the Pythagorean Theorem on the Coordinate Plane 149
Dup
licat
ing
any
part
of t
his
book
is p
rohi
bite
d by
law
.
On the town map at right, each unit represents 1 kilometer. Use the town map to answer questions 8 and 9.
8. MaksimjogsdirectlyfromCityHalltothepubliclibrary .Howmanykilometersdoeshejog?Showyourwork .
9. Acrowfliesdirectlyfromthecourthousetothemuseum .Whatdistancedoesthecrowfly?Showyourwork .
Plot the points on the coordinate plane. Then calculate the distance between the two points. Round your answer to the nearest tenth. Show your work.
10. pointV(25,2)andpointW(1,22)
Solve.
11. DRAW DrawadiagonalforrectangleABCDandcalculateitslength .Isitpossibletodrawadifferentdiagonalforthisrectanglethathasadifferentlength?Explain .
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A D
12. COMPARE Compare___
PQ to___
PR .Whichlinesegmentislonger?Howmanyunitslonger?Showyourwork .
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City HallMonument
Park
School
CourthousePublic Library
Museum
Town Map
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