Question

Slopes of perpendicular lines are _____.

a. negative reciprocals
b. the same
c. reciprocals
d. opposites

Answer 1

Correct: Option a. negative reciprocals

Explanation:

Perpendicular lines are defined as those who intersect at an angle of 90°.

There is an easy way to find out if two equations of lines correspond to perpendicular lines or not.

If line 1 is

y=m1x+b1

And line 2 is:

y=m2x+b2

The condition for the lines to be perpendicular is that:

m1*m2=-1

Solving for m2:

`\displaystyle m2 = -(1)/(m1)`

As seen, both slopes are negative reciprocals.

Correct: Option a. negative reciprocals