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

Answer:

Option C is the correct option.

Step-by-step explanation:

Considering the triangle ABC, the slope of the line CA is given by $\frac{AB}{BC} = \frac{6 - 3}{-3 - (- 1)}$

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

$\frac{CD}{DE} = \frac{3 - (- 3)}{- 1 - 3 }$

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

$\frac{6 - 3}{-3 - (- 1)} = \frac{3 - (- 3)}{- 1 - 3 }$

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