To find which of these lines are perpendicular, find the slope of each line.
To do it, use 2 points on the line and the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
AB:
[tex]m=\frac{5-2}{4-(-5)}=\frac{3}{9}=\frac{1}{3}[/tex]
BC:
[tex]m=\frac{-1-5}{5-4}=-6[/tex]
CD:
[tex]m=\frac{-1-(-4)}{5-(-3)}=\frac{3}{7}[/tex]
DA:
[tex]m=\frac{-4-2}{-3-(-5)}=-\frac{6}{2}=-3[/tex]
For 2 lines to be perpendicular, the product of their slopes must be -1. According to this the only pair that meets this condition is AB, DA.
[tex]m=\frac{1}{3}\cdot-3=-1[/tex]
Segment AB and DA are perpendicular.
