Question

triangle dog is the image that resulted from a dilation of triangle cat. the center of dilation is the point. the scale factor is

Explanation:

Step1: Identify center of dilation

The center of dilation is the point that stays fixed during the dilation. By observing the graph, we can see that the lines connecting corresponding points of $\triangle CAT$ and $\triangle DOG$ intersect at the origin $(0,0)$. So the center of dilation is $(0,0)$.

Step2: Calculate scale - factor

Let's take a pair of corresponding sides. For example, consider the distance between two points on $\triangle CAT$ and $\triangle DOG$. Let's take the horizontal distance of side $CA$ and $DO$. The length of $CA$: If $C(-6,4)$ and $A(2,2)$, using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, we have $CA=\sqrt{(2 + 6)^2+(2 - 4)^2}=\sqrt{64 + 4}=\sqrt{68}$. For $DO$, if $D(- 3,2)$ and $O(1,1)$, $DO=\sqrt{(1 + 3)^2+(1 - 2)^2}=\sqrt{16+1}=\sqrt{17}$. The ratio of the lengths of corresponding sides $DO$ to $CA$ is $\frac{DO}{CA}=\frac{\sqrt{17}}{\sqrt{68}}=\frac{1}{2}$. So the scale - factor is $\frac{1}{2}$.

Answer:

The center of dilation is the point $(0,0)$
The scale factor is $\frac{1}{2}$