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About Perpendicular Lines

What are Perpendicular Lines?

Perpendicular lines are two lines that intersect at a right angle (90 degrees). They form a cross shape when they meet.

Formula for Perpendicular Lines

If the slope of one line is \(m\), the slope of its perpendicular line is the negative reciprocal:

Where:

• \(m\) is the slope of the original line
• \(m_{\text{perpendicular}}\) is the slope of the perpendicular line

Calculation Steps

1. Identify the slope \(m\) of the original line
2. Calculate the negative reciprocal: \(-\frac{1}{m}\)
3. The result is the slope of the perpendicular line

Example

Let's find the perpendicular line to a line with slope 2:

1. Original slope: \(m = 2\)
2. Perpendicular slope: \(m_{\text{perpendicular}} = -\frac{1}{2} = -0.5\)