Check whether the given dilationis a similarity transformation or not.Given:The given dilation is12210202901.jpg

Calculation:
From the figure, the given vertices are
A(0,0),B(-4,-4),C(4,-2),D(-2,-2),E(2,-1)
Find the distance (using distance formula) of corresponding sides and find the ratio.
${\displaystyle AB=\sqrt{{(-4-0)}^2+{(-4-0)}^2}=\sqrt{32}=4\sqrt{2}}$
${\displaystyle AD=\sqrt{{(-2-0)}^2+{(-2-0)}^2}=\sqrt{8}=2\sqrt{2}}$
${\displaystyle \frac{AD}{AB}=\frac{2\sqrt{2}}{4\sqrt{2}}=\frac{1}{2}}$
${\displaystyle AC=\sqrt{{(4-0)}^2+{(-2-0)}^2}=\sqrt{20}=2\sqrt{5}}$
${\displaystyle AE=\sqrt{{(2-0)}^2+{(-1-0)}^2}=\sqrt{5}}$
${\displaystyle \frac{AE}{AC}=\frac{\sqrt{5}}{2\sqrt{5}}=\frac{1}{2}}$
${\displaystyle BC=\sqrt{{[4-(-4)]}^2+{[-2-(-4)]}^2}=\sqrt{68}=2\sqrt{17}}$
${\displaystyle DE=\sqrt{{[2-(-2)]}^2+{[-1-(-2)]}^2}=\sqrt{17}}$
${\displaystyle \frac{DE}{BC}=\frac{\sqrt{17}}{2\sqrt{17}}=\frac{1}{2}}$
From the above result, the lenght of the sides are proportional.
By the use of SSS similarity,
${\displaystyle \mathrm{△}ADE\sim \mathrm{△}ABC}$.
Hence the given dilation is a similarity transformation.