Solved: "Draw a graph for the original figure and..."

midtlinjeg

Answered question

2020-11-20

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
V(-3,4),W(-5,0),X(1,2),Y(-6,-2),Z(3,1)

Answer & Explanation

firmablogF

Skilled2020-11-21Added 92 answers

Calculation:
The graph for the given points V(-3,4),W(-5,0),X(1,2),Y(-6,-2),Z(3,1) is given below.

Find the distance(using distance formula)of corresponding sides and find the ratio.
$V Y = \sqrt{{[- 3 - (- 6)]}^{2} + {[4 - (- 2)]}^{2}} = \sqrt{45} = 3 \sqrt{5}$
$V W = \sqrt{{[- 3 - (- 5)]}^{2} + {(4 - 0)}^{2}} = \sqrt{20} = 2 \sqrt{5}$
$\frac{V W}{V Y} = \frac{2 \sqrt{5}}{3 \sqrt{5}} = \frac{2}{3}$
$V Z = \sqrt{{(- 3 - 3)}^{2} + {(4 - 1)}^{2}} = \sqrt{45} = 3 \sqrt{5}$
$V X = \sqrt{{(- 3 - 1)}^{2} + {(4 - 2)}^{2}} = \sqrt{20} = 2 \sqrt{5}$
$\frac{V X}{V Z} = \frac{2 \sqrt{5}}{3 \sqrt{5}} = \frac{2}{3}$
$∠ V \tilde{=} ∠ V$
From the above result, the lenght of the sides are proportional and the angles between them are congruent.
By the use of SAS similarity,
$△ A D E \sim △ A B C$ .
Hence the dilation is a similarity transformation.

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