Question

Which lines are perpendicular?

Answer 1

Given:

Line A: $y=\frac{1}{2} x+2$

Line B: $y=\frac{-1}{2} x+7$

Line C: $y=2 x+4$

Line D: $y=\frac{1}{2} x+\frac{5}{4}$

To find:

Which lines are perpendicular

Solution:

General equation of a line:

y = mx + c

where m is the slope and c is the y-intercept.

Slope of line A = $\frac{1}{2}$

Slope of line B = $\frac{-1}{2}$

Slope of line C = 2

Slope of line D = $\frac{1}{2}$

Two lines are perpendicular if their slopes are negative reciprocal of one another.

$\Rightarrow m_1=\frac{-1}{m_2}$

$\frac{-1}{2}=-(-2)=2$

Negative reciprocal of $\frac{-1}{2}$ is 2.

Therefore line B and line C are perpendicular lines.