The vertices of a right triangle are (–3, 5), (4, –1), and (4, y).

What is the value of y?

A. -3

B. -1

C. 4

D. 5


We call A(–3, 5), B(4, –1), and C(4, y), the triangle ABC. We have the coordinates of three vectors: AB(7, -6), BC(0; y+1), and AC(7, y-5) Cause this triangle can be right at A, B or C, we have three cases: + Right at A: AB.AC=0 or 7x7+(-6)x(y-5)=0 and we have 49-6y+30=0 or y=79/6 + Right at B: AB.BC=0 or 7x0+(-6)x(y+1)=0 and we have 0-6y-6=0 or y=-1 Right at C: BC.AC=0 or 0x7+(y+1)x(y-5)=0 and we have (y+1)x(y-5)=0 or y=-1 or y=5 Then, we have 3 values of y.

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