Question

the triangle tuv is a dilation of the triangle tuv. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Identify corresponding points

Original points: $T(3,0)$, $V(3,6)$, $U(5,-6)$
Image points: $T'(2,0)$, $V'(2,4)$, $U'(4,-4)$

Step2: Calculate scale factor

Use coordinates of $T$ and $T'$:
$\text{Scale factor} = \frac{\text{Image }x\text{-coordinate}}{\text{Original }x\text{-coordinate}} = \frac{2}{3}$
Verify with $V$ and $V'$: $\frac{4}{6} = \frac{2}{3}$
Verify with $U$ and $U'$: $\frac{4}{5}$ (x-coordinate) no, use y-coordinate: $\frac{-4}{-6} = \frac{2}{3}$

Answer:

$\frac{2}{3}$