Question

and triangle jkl are similar right triangles. which proportion can be used to show that the slope of $overline{jl}$ is equal to the slope of $overline{mp}$?
a. $\frac{0 - (-7)}{4 - (-4)}=\frac{-4 - (-10)}{8 - (-1)}$
b. $\frac{0 - 4}{-4 - (-7)}=\frac{-4 - 8}{-1 - (-10)}$
c. $\frac{0 - (-4)}{4 - (-7)}=\frac{-4 - (-1)}{8 - (-10)}$
d. $\frac{-4 - (-7)}{0 - 4}=\frac{-1 - (-10)}{-4 - 8}$

Explanation:

Step1: Recall slope formula

Slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. For similar right - triangles, slopes are equal.

Step2: Check options

For two similar right - triangles, the ratios of vertical change to horizontal change should be equal. Option A has correct ratio setup for showing equal slopes.

Answer:

A. $\frac{0-(-7)}{4-(-4)}=\frac{-4-(-10)}{8-(-1)}$