Draw a graph for the original figure and its dilated image. Check whether the dilation is a similarity transformation or not. Given: The given vertices are J(-6,8),K(6,6),L(-2,4),D(-12,16),G(12,12),H(-4,8)

foass77W 2021-02-13 Answered
Draw a graph for the original figure and its dilated image. Check whether the dilation is a similarity transformation or not.
Given:
The given vertices are
J(-6,8),K(6,6),L(-2,4),D(-12,16),G(12,12),H(-4,8)
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Expert Answer

pattererX
Answered 2021-02-14 Author has 95 answers

Calculation:
The graph for the given points J(-6,8),K(6,6),L(-2,4),D(-12,16),G(12,12),H(-4,8) is given below.
image
Find the distance(using distance formula)of corresponding sides and find the ratio.
DH=[12(4)]2+[168]2=128=82
JL=[6(2)]2+(84)2=32=42
DHJL=8242=2
GH=[12(4)]2+(128)2=272=417
KL=[6(2)]2+(64)2=68=217
GHKL=417217=2
DG=[1212)2+(1612)2)=592=437
JK=[66]2+(86)2=148=237
DGJK=437237=2
From the above result, the lenght of the sides are proportional and the angles between them are congruent.
By the use of SSS similarity,
JLKDHG.
Hence the dilation is a similarity transformation.

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