Question

triangle tuv was dilated to create triangle tuv using point a as the center of dilation. what is the scale factor of the dilation? 3.2, 4.8, options: 2/5, 2/3, 3/2, 8/5

Explanation:

Step1: Identify corresponding segments

Scale factor = $\frac{\text{length of image segment}}{\text{length of pre-image segment}}$. Use segments from center A: $AT'$ (image) and $AT$ (pre-image)? No, use $AU'$ and $AU$: $AU'=2$, $AU=3$? Wait, check $AV'$ and $AV$: $AV'=3$, $AV=4.8$? No, correct: image is smaller $\triangle T'U'V'$, pre-image $\triangle TUV$. $AU'=2$, $AU=3$ → ratio $\frac{2}{3}$.

Step2: Confirm scale factor

$\frac{AT'}{AT}=\frac{AU'}{AU}=\frac{AV'}{AV}=\frac{2}{3}$.

Answer:

B. $\frac{2}{3}$