Answer: The required scale factor of dilation is 2.
Step-by-step explanation: We are given to find the scale factor of dilation shown in the figure.
From the figure, we see that
triangle ABC is dilated to triangle A'B'C', where the co-ordinates of the points A, B, A' and B' are (2, 3), (2, -2), (4, 6) and (4, -4) respectively.
So, the lengths of the sides AB and A'B' can be calculated using distance formula as follows :
\(AB=\sqrt{(2-2)^2+(-2-3)^2}=\sqrt{25}=5~\textup{units},\\\\A'B'=\sqrt{(4-4)^2+(-4-6)^2}=\sqrt{100}=10~\textup{units}.\)
We know that
the scale factor of dilation is defined as
\(S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.\)
Therefore, the scale factor of the given dilation will be
\(S=\dfrac{A'B'}{AB}=\dfrac{10}{5}=2.\)
Thus, the required scale factor is 2.
