Question

triangle abc is dilated to form △abc. what is the dilation factor? what is the center of dilation? select all that apply.
a. dilation factor of 3
b. dilation factor of ⅓
c. center of dilation (-6, 5)
d. center of dilation (6, -5)

Explanation:

Step1: Find dilation factor

Count the distance between corresponding points. For example, if we consider the horizontal distance of a vertex of $\triangle ABC$ and its corresponding vertex of $\triangle A'B'C'$. Let's take point $A$ and $A'$. The horizontal distance from $A$ to $A'$ shows that the new - figure is 3 times the size of the original. So the dilation factor is 3.

Step2: Find center of dilation

The center of dilation is the point about which the figure is dilated. By observing the graph, we can see that the lines connecting corresponding points (e.g., $AA'$, $BB'$, $CC'$) intersect at the point $(-6,5)$. So the center of dilation is $(-6,5)$.

Answer:

A. Dilation factor of 3
C. Center of dilation $(-6,5)$