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)

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.
${\displaystyle VY=\sqrt{{[-3-(-6)]}^2+{[4-(-2)]}^2}=\sqrt{45}=3\sqrt{5}}$
${\displaystyle VW=\sqrt{{[-3-(-5)]}^2+{(4-0)}^2}=\sqrt{20}=2\sqrt{5}}$
${\displaystyle \frac{VW}{VY}=\frac{2\sqrt{5}}{3\sqrt{5}}=\frac{2}{3}}$
${\displaystyle VZ=\sqrt{{(-3-3)}^2+{(4-1)}^2}=\sqrt{45}=3\sqrt{5}}$
${\displaystyle VX=\sqrt{{(-3-1)}^2+{(4-2)}^2}=\sqrt{20}=2\sqrt{5}}$
${\displaystyle \frac{VX}{VZ}=\frac{2\sqrt{5}}{3\sqrt{5}}=\frac{2}{3}}$
${\displaystyle \mathrm{\angle }V\stackrel{\sim }{=}\mathrm{\angle }V}$
From the above result, the lenght of the sides are proportional and the angles between them are congruent.
By the use of SAS similarity,
${\displaystyle \mathrm{△}ADE\sim \mathrm{△}ABC}$.
Hence the dilation is a similarity transformation.