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) 6 − 3
−3 − 1
= 3 − (−3)
−1 − 3

B) 6 − 3
−3 − (−1)
= 3 − 3
−1 − 3

C) 6 − 3
−3 − (−1)
= 3 − (−3)
−1 − 3

D) −3 − (−1)
6 − 3
= 3 − (−3)
−1 − 3

Answer 1

C) 6 − 3

−3 − (−1)

= 3 − (−3)

−1 − 3

Explanation:

Answer 2

Option C is the correct option.

Explanation:

Considering the triangle ABC, the slope of the line CA is given by
`(AB)/(BC) = (6 - 3)/(-3 - (- 1))`

Again, considering the triangle CDE, the slope of the line EC is given by

`(CD)/(DE) = (3 - (- 3))/(- 1 - 3 )`

Since CA and EC represents the same straight line so, we can write

`(6 - 3)/(-3 - (- 1)) = (3 - (- 3))/(- 1 - 3 )`

Therefore, option C is the correct option. (Answer)