Answer:
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).
