Triangle abc is similar to triangle ade, which is formed with angle a and side ad, as shown. what could be the coordinates of point e? (2,–1) (–1,2) (–3,–1) (–1,–3)

Only option B is correct, i.e. (-1, 2).

Step-by-step explanation:

Two triangles are similar when their corresponding angles are congruent.

Triangle ABC would be similar to triangle ADE when ∠A = ∠A, ∠B = ∠D, and ∠C = ∠E.

Since A is common vertex and D is on side AB, then it is sure that E would be on side AC.

The information ∠B = ∠D, and ∠C = ∠E makes sure that DE║BC.

It means slope of DE = slope of BC.

⇒ (y-3)/(x-2) = (-4+1)/(-5-4)

⇒ (y-3)/(x-2) = (-3)/(-9)

⇒ (y-3)/(x-2) = 1/3

We can try and plug all four options in the proportion and check which one satisfy the equation.

option A: (-1-3)/(2-2) ≠ 1/3

option B: (2-3)/(-1-2) = 1/3

option C: (-1-3)/(-3-2) ≠ 1/3

option D: (-3-3)/(-1-2) ≠ 1/3

Hence, only option B is correct, i.e. (-1, 2).

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