Given points P(2,-1), Q(-4, 2), and M(5,3), find coordinates of a point K such that MK is perpendicular to PQ.

Question

Given points P(2,-1), Q(-4, 2), and M(5,3), find coordinates of a point K such that MK is perpendicular to PQ.

Answer 1

The slope of PQ is (2+1)/(-4-2) = 3/-6 = -1/2

The slope of any line perpendicular to PQ will thus be 3.

Now you have a point and a slope. The line perpendicular to PQ and passing through M is

(y-3)/(x-5) = 3