Find x- and y-values that make ABP a right angle.

Question

A = (3,2), B = (1,5), and P = (x,y). Find x- and y-values that make ABP a right angle.

Answer 1

A(3,2), B(1,5) and P(x,y) form a right triangle

slope of AB is (5-2)/(1-3) = 3/-2 = -3/2

a perpendicular line has slope 2/3

an equation perpendicular to AB, through A is (y-2) =(2/3)(x-3) or y = (2/3)x + 2

any point on that line will form a right triangle ABP, such as P(0,2)

there are an infinite number of possible points P on that line that all will form a right triangle

an equation perpendicular to AB through B is (y-5) = (2/3)(x-1) or y = (2/3)x + 13/3

any point on that line will form a right triangle ABP such as P(0, 13/3)

there are two other right triangles using AB as the hypotenuse

either P(5,2) or (1,2) where ABP will form a right triangle

It may help to sketch the lines and points