Question

Are the lines AB and CD perpendicular if the points defining the lines have coordinates of A(3,-2) B(6,13) C(-5,8) and D(5,6)? Justify your answer.

Answer 1

we find the slopes of the lines:

first line

$\text{slope}=\frac{y2-y1}{x2-x1}=\frac{13-(-2)}{6-3}=\frac{13+2}{3}=\frac{15}{3}=5$

second lline

$\text{slope}=\frac{6-8}{5-(-5)}=-\frac{2}{5+5}=-\frac{2}{10}=-\frac{1}{5}$

then, Two lines are perpendicular if & only if the product of their slopes equals -1, which is the case for 5 and -1/5.

answer: the lines are perpendicular