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 original rarr A(2,3),B(0,1),C(3,0) image rarr D(4,6),F(0,2),G(6,0)

abondantQ 2020-10-27 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
original A(2,3),B(0,1),C(3,0)
image D(4,6),F(0,2),G(6,0)
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Expert Answer

davonliefI
Answered 2020-10-28 Author has 79 answers

Calculation:
The graph for the points is given below.
image
Find the distance (using distance formula) of corresponding sides and find the ratio.
AB=(20)2+(31)2=8=22
DF=(40)2+(62)2=32=42
ABDF=2242=12
AC=(23)2+(30)2=10
DG=(46)2+(60)2=40=210
ACDG=10210=12
BC=(03)2+(10)2=10
FG=(06)2+(20)2=40=210
BCFG=10210=12
From the above result, the lenght of the sides are proportional.
By the use of SSS similarity,
DFGABC.
Hence the dilation is a similarity transformation.

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