How do you know if two lines are perpendicular

Asked by maham237 @ 23/02/2021 in Mathematics viewed by 287 People

How to tell if two lines are perpendicular

Answered by maham237 @ 23/02/2021

ANSWER

The two lines are perpendicular if $m_1 \times m_2 = - 1$

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

$y = - \frac{1}{2} x + 1$

has slope

$m_2 = - \frac{1}{2}$

The product of the two slopes is

$m_1 \times m_2 = 2 \times - \frac{1}{2}$

This implies that:

$m_1 \times m_2 = - 1$

Therefore the two lines are perpendicular.

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