Find a value for m so AB is perpendicular to CD

Question

Consider 4 points A (-1,3), B(3,-2), C(2,1) and D(-3,m). Find a value for M so AB is perpendicular to CD

Answer 1

m =29/4 = 7.25

(-3,m) and (2,1) have a line through them with slope = (m-1)/(-3-2) = (m-1)/(-5)

that's the slope of CD

slope of the line through AB is -5/4

set the slopes equal, in order for the lines to be parallel

(m-1)/(-5)= -5/4

cross multiply

4m-4 = 25

4m = 29

m = 29/4