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}=(y2-y1)/(x2-x1)=(13-(-2))/(6-3)=(13+2)/(3)=(15)/(3)=5`

second lline

`\text{slope}=(6-8)/(5-(-5))=-(2)/(5+5)=-(2)/(10)=-(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