Question

if you have the points a(5,7) b(-1,-1) and p(x,y). how would you write an equaiton for all x and y for which pa is perpendicular to pb.

Answer 1

Best I can come up with is:

(py - by)/(px - bx) = -1 [(px - ax) / (py - ay)]

It relates the slopes of two perpendicular lines: each line's slope is the negative reciprocal of the others.

The problem arises when one of the slopes is 0, because then the (negative) reciprocal is some number over 0, which is undefined.

Answer 2

Best I can come up with is:

(py - by)/(px - bx) = -1 [(px - ax) / (py - ay)]

It relates the slopes of two perpendicular lines: each line's slope is the negative reciprocal of the others.

The problem arises when one of the slopes is 0, because then the (negative) reciprocal is some number over 0, which is undefined.

Anyway, pluggin in we get:

(py - (-1))/(px - (-1)) = -1 [(px - 5) / (py - 7)]


(py + 1)/(px + 1) = -1 [(px - 5) / (py - 7)]