How to tell if two lines are perpendicular

Question

asked Mar 14, 2020 180k views

2 Answers

Tim Siegel · Answer 1 · 2020-03-20T03:27:01+0000

ANSWER

The two lines are perpendicular if
m_1 * m_2 = - 1

EXPLANATION

Given two lines:

y=m_1x+b_1

and

y=m_2x+b_2

We can tell wether these two lines are perpendicular to each other using their slopes.

If the product of their slopes is -1, the then the two line are perpendicular.

For example:

The line

y = 2x + 6

has slope

m_1= 2

and the line

y = - (1)/(2) x + 1

has slope

m_2 = - (1)/(2)

The product of the two slopes is

m_1 * m_2 = 2 * - (1)/(2)

This implies that:

m_1 * m_2 = - 1

Therefore the two lines are perpendicular.