# Parallel and perpendicular lines

If two non-vertical lines that are in the same plane has the same slope, then they are said to be parallel. Two parallel lines won't ever intersect.

If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular. Horizontal and vertical lines are perpendicular to each other i.e. the axes of the coordinate plane.

**Example**

Compare the slope of the perpendicular lines

The slope of the red line:

$$m_{1}=\frac{-3-2}{2-\left ( -3 \right )}=\frac{-5}{5}=-1$$

The slope of the blue line

$$m_{2}=\frac{2-\left ( -2 \right )}{3-\left ( -1 \right )}=\frac{4}{4}=1$$

The slopes of two perpendicular lines are negative reciprocals.

The product of the slopes of two perpendicular lines is -1 since

$$m\cdot -\frac{1}{m}=-1,\: \: where\: \: m_{1}=m\: \: and\: \: m_{2}=-\frac{1}{m}$$

**Video lesson**

Are these two line parallel?