Answer: The required scale factor of dilation is 3.
Step-by-step explanation: Given that the dashed triangle is the image of the solid triangle and the center of dilation is (-4, -4).
We are to find the scale factor that is used to create the dilation.
We know that the scale factor of dilation is given by
[tex]S=\dfrac{\textup{length of a side of the dilated triangle}}{\textup{length of the corresponding side of the original triangle}}.[/tex]
From the graph, we note that
two vertices of the original triangle are (-4, -4) and (-4, -6).
And, the corresponding two vertices of the dilated triangle are (-4, -4)and (-4, 2).
So, the length of a side of the original triangle, as calculated using distance formula is
[tex]d_1=\sqrt{(-4+4)^2+(-6+4)^2}=\sqrt{0+4}=2[/tex]
and the length of the corresponding side of the dilated triangle is
[tex]d_2=\sqrt{(-4+4)^2+(2+4)^2}=\sqrt{0+36}=6[/tex]
Therefore, the scale factor of dilation is
[tex]S=\dfrac{d_2}{d_1}=\dfrac{6}{2}=3.[/tex]
Thus, the required scale factor of dilation is 3.
