Answer: The answers are:
(a) The dilation is a reduction of the original figure.
(b) The scale factor of dilation is [tex]\dfrac{2}{3}.[/tex]
Step-by-step explanation: We are given a dilation from ΔMSV to ΔM'S'V'.
We are to check whether the dilation is a reduction or an enlargement of the original figure. Also, to find the scale factor of dilation.
We know that if a figure is dilated to form the image figure, then the scale factor of dilation is given by
[tex]S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]
The dilation will be a reduction if S < 1 and it will be an enlargement if S > 1.
From the figure, we note that
the co-ordinates of the vertices of the original triangle MSV are M(-3, 3), S(6, 3) and V(3, -3),
and the co-ordinates of the dilated triangle M'S'V' are M'(-2, 2), S'(4, 2) and V'(2, -2).
So, the lengths of the corresponding sides MS and M'S' of both the original and dilated figures are calculated using distance formula as follows:
[tex]MS=\sqrt{(6+3)^2+(3-3)^2}=\sqrt{9^2}=9,\\\\M'S'=\sqrt{(4+2)^2+(2-2)^2}=\sqrt{6^2}=6.[/tex]
Therefore, the scale factor of dilation is given by
[tex]S=\dfrac{M'S'}{MS}\\\\\\\Rightarrow S=\dfrac{6}{9}\\\\\\\Rightarrow S=\dfrac{2}{3}.[/tex]
Since S < 1, so the dilation is a reduction.
Thus,
(a) The dilation is a reduction of the original figure.
(b) The scale factor of dilation is [tex]\dfrac{2}{3}.[/tex]
