Question

Consider the figure on the left. Which lines are perpendicular?

Answer 1

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:

`m=(y2-y1)/(x2-x1)`

AB:

`m=(5-2)/(4-(-5))=(3)/(9)=(1)/(3)`

BC:

`m=(-1-5)/(5-4)=-6`

CD:

`m=(-1-(-4))/(5-(-3))=(3)/(7)`

DA:

`m=(-4-2)/(-3-(-5))=-(6)/(2)=-3`

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.

`m=(1)/(3)\cdot-3=-1`

Segment AB and DA are perpendicular.