Question

What is the scale factor of the dilation

Answer 1

The scale factor is 2. I looked at point I then I' and point I was at 2/3 and I' was at 4/6 and so
2/3*2 is 4/6.

Answer 2

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.