# 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)

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