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 M(1,4), P(2,2), Q(5,5), S(-3,6),T(0,0),U(9,9)

Calculation:
The graph for the given points M(1,4), P(2,2), Q(5,5), S(-3,6),T(0,0),U(9,9) is given below.

Find the distance(using distance formula) of corresponding sides and find the ratio.
${\displaystyle ST=\sqrt{{(-3-0)}^2+{(6-0)}^2}=\sqrt{45}=3\sqrt{5}}$
${\displaystyle MP=\sqrt{{(1-2)}^2+{(4-2)}^2}=\sqrt{5}}$
${\displaystyle \frac{MP}{ST}=\frac{\sqrt{5}}{3\sqrt{5}}=\frac{1}{3}}$
${\displaystyle SU=\sqrt{{(-3-9)}^2+{(6-9)}^2}=\sqrt{153}=3\sqrt{17}}$
${\displaystyle MQ=\sqrt{{(1-5)}^2+{(4-5)}^2}=\sqrt{17}}$
${\displaystyle \frac{MQ}{SU}=\frac{\sqrt{17}}{3\sqrt{17}}=\frac{1}{3}}$
${\displaystyle TU=\sqrt{{(0-9)}^2+{(0-9)}^2}=\sqrt{162}=9\sqrt{2}}$
${\displaystyle PQ=\sqrt{{(2-5)}^2+{(2-5)}^2}=3\sqrt{2}}$
${\displaystyle \frac{PQ}{TU}=\frac{3\sqrt{2}}{9\sqrt{2}}=\frac{1}{3}}$
From the above result, the lenght of the sides are proportional.
By the use of SSS similarity,
${\displaystyle \mathrm{△}MPQ\sim \mathrm{△}STU}$.
Hence the dilation is a similarity transformation.