Question

Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?
A)
3 − 5
−4 − 0
=
3 − 2
0 − 2


B)
3 − 5
−4 − 0
=
3 − 2
2 − 0


C)
5 − 3
−4 − 0
=
3 − 2
0 − 2


D)
5 − 3
−4 − 0
=
2 − 3
0 − 2

Answer 1

I answered this question on one of my test. the answer is C.

Answer 2

Answer: The proportion (5-3) / (-4-0) = (3-2) / (0-2) can be used to show that the slope of AC in triangle ABC is equal to the slope of CE in triangle CDE, where these triangles are similar right triangles.

Option C) (5-3) / (-4-0) = (3-2) / (0-2)

Solution

Slope of AC: mac=(ya-yc)/(xa-xc)

A=(-4,5)=(xa,ya)→xa=-4, ya=5

C=(0,3)=(xc,yc)→xc=0, yc=3

mac=(5-3)/(-4-0)

Slope of CE: mce=(yc-ye)/(xc-xe)

C=(0,3)=(xc,yc)→xc=0, yc=3

E=(2,2)=(xe,ye)→xe=2, ye=2

mce=(3-2)/(0-2)

mac=mce

(5-3) / (-4-0) = (3-2) / (0-2)