Question

triangles pqr and rst are similar right triangles. which proportion can be used to show that the slope of $overline{pr}$ is equal to the slope of $overline{rt}$? f $\frac{3 - 7}{-4-(-7)}=\frac{-5 - 3}{2-(-4)}$ g $\frac{3-(-4)}{7-(-7)}=\frac{-5 - 2}{3-(-4)}$ h $\frac{-4-(-7)}{3 - 7}=\frac{2-(-4)}{-5 - 3}$ j $\frac{-4-(-3)}{-7 - 7}=\frac{2-(-5)}{-4 - 3}$

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify points on $\overline{PR}$ and $\overline{RT}$

Let's assume $P(-7,7)$, $R(-4,3)$ and $T(2, - 5)$. The slope of $\overline{PR}$ is $m_{PR}=\frac{3 - 7}{-4-(-7)}$, and the slope of $\overline{RT}$ is $m_{RT}=\frac{-5 - 3}{2-(-4)}$.

Step3: Check the proportion

The proportion that shows the slope of $\overline{PR}$ is equal to the slope of $\overline{RT}$ is $\frac{3 - 7}{-4-(-7)}=\frac{-5 - 3}{2-(-4)}$.

Answer:

F. $\frac{3 - 7}{-4-(-7)}=\frac{-5 - 3}{2-(-4)}$