Question

This is the same dilation that you use in question three. What scale factor was used to create the dilated triangle MSV’? In your answer, keep the scale factor that was used in explain how you calculated.

Answer 1

Given:

The coordinates of a triangle MSV are, M(-3,3), S(6,3), and V(3, -3).

The coordinates of a triangle M'S'V' are, M'(-2,2), S'(4,2), and V'(2, -2).

To find the scale factor:

Using the scale factor formula,

`\text{Scale factor=}\frac{The\text{ length of the new side}}{\text{The length of the old side}}`

The length of the new side M'S' is

`\begin{gathered} M^(\prime)S^(\prime)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{(4-(-2))^2+(2-2)^2} \\ =\sqrt[]{(4+2)^2+0} \\ =\sqrt[]{6^2} \\ =6 \end{gathered}`

The length of the old side MS is

`\begin{gathered} MS=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{(6-(-3))^2+(3-3)^2} \\ =\sqrt[]{(6+3)^2+0} \\ =\sqrt[]{9^2} \\ =9 \end{gathered}`

Then, the scale factor is,

`\begin{gathered} \frac{New\text{ length}}{\text{Old length}}=(6)/(9) \\ =(2)/(3) \end{gathered}`

Hence, the scale factor is,

`(2)/(3)`