posted by Alone3030 .
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.
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