Name: _________________________________________________ Determining Scale using Coordinate Points Scale is determined by comparing an image (the new figure) to its pre-image (the original figure) using a fraction. Basically, = !"# !"# . This formula applies whether you are using side lengths or x-y points. Remember, the prime symbol (‘) is used to identify the image (new figure). Example: Determine the scale factor of the dilated figure using the given points. (20, 36), (8, 28), (20, 16), ′ 5, 9 , ′ 2, 7 & ′ 5, 4 Since the problem uses the term “dilated figure,” you know that the figures are similar (which means you do not need to check the scale). Pick any point and its match to create the scale. New: ′ 5, 9 Old: 20, 36 = ! = (5, 9) (20, 36) : 5 20 & 9 36 : 5 ÷ 5 20 ÷ 5 = 1 4 & 9 ÷ 9 36 ÷ 9 = 1 4 The scale factor is ! ! . Determine the scale factor of each dilated figure using the given points. 1. 2, 4 & ′(5, 10) 2. 5, 10 & ′(2, 4) 3. ! 6, 15 & (8, 20) 4. ! 8, 20 & (6, 15) 5. 12, 18 & ′(28, 42) 6. ! 12, 18 & (28, 42) 7. ! 2, 10 , ! 16, 6 , ! 4, 18 , 9, 45 , 72, 27 & (18, 81) 8. 2, 10 , 16, 6 , 4, 18 , ′ 9, 45 , ′ 72, 27 & ′(18, 81) 9. ! 36, 44 , ! 8, 40 , ! 48, 24 , 27, 33 , 6, 30 & (36, 18) 10. 11. 12. : 1. 5 2 2. 2 5 3. 3 4 4. 4 3 5. 7 3 6. 3 7 7. 2 9 8. 9 2 9. 4 3 10. 1 2 11. 3 1 12. 3 2 A B C C' A' B' D E F F' D' E' G H J J' H' G'

55. Determining Scale using Coordinate Points ...mathbygrosvenor.weebly.com/uploads/1/3/4/8/13488403/55._determ… · !′2,7 & !′5,4 Since the problem uses the term “dilated

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Page 1: 55. Determining Scale using Coordinate Points ...mathbygrosvenor.weebly.com/uploads/1/3/4/8/13488403/55._determ… · !′2,7 & !′5,4 Since the problem uses the term “dilated

Name:_________________________________________________

DeterminingScaleusingCoordinatePointsScaleisdeterminedbycomparinganimage(thenewfigure)toitspre-image(theoriginalfigure)usingafraction.Basically,𝑠𝑐𝑎𝑙𝑒 = !"#

!"#.Thisformulaapplieswhetheryouareusingsidelengthsorx-ypoints.Remember,theprime

symbol(‘)isusedtoidentifytheimage(newfigure).

Example:Determinethescalefactorofthedilatedfigureusingthegivenpoints.𝑋(20, 36), 𝑌(8, 28), 𝑍(20, 16),𝑋′ 5, 9 ,𝑌′ 2, 7 & 𝑍′ 5, 4 Sincetheproblemusestheterm“dilatedfigure,”youknowthatthefiguresaresimilar(whichmeansyoudonotneedto

checkthescale).Pickanypointanditsmatchtocreatethescale.New:𝑋′ 5, 9 Old:𝑋 20, 36

𝑆𝑐𝑎𝑙𝑒 =𝑋!

𝑋=

(5, 9)(20, 36)

𝑆𝑝𝑙𝑖𝑡 𝑢𝑝: 520

& 936

𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦: 5 ÷ 520 ÷ 5

=14

& 9 ÷ 936 ÷ 9

=14

Thescalefactoris!!.

Determinethescalefactorofeachdilatedfigureusingthegivenpoints.1.𝐴 2, 4 & 𝐴′(5, 10) 2.𝐵 5, 10 & 𝐵′(2, 4) 3.𝐶! 6, 15 & 𝐶(8, 20)

4.𝐷! 8, 20 & 𝐷(6, 15) 5.𝐸 12, 18 & 𝐸′(28, 42) 6.𝐹! 12, 18 & 𝐹(28, 42)

7.𝐺! 2, 10 ,𝐻! 16, 6 , 𝐼! 4, 18 , 𝐺 9, 45 ,𝐻 72, 27 & 𝐼(18, 81)

8.𝐺 2, 10 ,𝐻 16, 6 , 𝐼 4, 18 , 𝐺′ 9, 45 ,𝐻′ 72, 27 & 𝐼′(18, 81)

9.𝑀! 36, 44 ,𝑁! 8, 40 ,𝑃! 48, 24 , 𝑀 27, 33 ,𝑁 6, 30 & 𝑃(36, 18)

10.

11.

12.

𝐶𝑜𝑟𝑟𝑒𝑐𝑡 𝑆𝑐𝑎𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟𝑠: 1. 52

2. 25

3. 34

4. 43

5. 73

6. 37

7. 29

8. 92

9. 43

10. 12

11. 31

12. 32

ABC

A'B' D

E' GH

J J'

Page 2: 55. Determining Scale using Coordinate Points ...mathbygrosvenor.weebly.com/uploads/1/3/4/8/13488403/55._determ… · !′2,7 & !′5,4 Since the problem uses the term “dilated

Name:_________________________________________________

DeterminingifPartsareSimilarForeachtriangle,lookforsimilarparts.Remember,similaranglesarethesame&similarsidefractionsareequal.13.