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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.

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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

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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} \\

Videolesson: Are these two line parallel?

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