How to Calculate Perpendicular Slope
What is Perpendicular Slope?
Two lines are perpendicular if they meet at right angles (90°). The slope of a line perpendicular to a line with slope m is −1/m. This is used in geometry, navigation, and engineering.
Formula
If line 1 has slope m, perpendicular line has slope −1/m
- m₁
- slope of original line
- m₂
- slope of perpendicular line — m₂ = −1/m₁
Step-by-Step Guide
- 1If slope of line 1 is m, perpendicular slope = −1/m
- 2Product of perpendicular slopes = −1
- 3Horizontal line (m=0) ⊥ vertical line (undefined slope)
- 4Two non-vertical lines are perpendicular iff m₁ × m₂ = −1
Worked Examples
Input
m = 2
Result
Perpendicular slope = −½
Input
m = −3/4
Result
Perpendicular slope = 4/3
Frequently Asked Questions
What is the slope of a vertical line?
Vertical lines are undefined slope. A horizontal line (perpendicular) has slope 0.
What is the relationship between perpendicular slopes?
The product of perpendicular slopes is −1: m₁ × m₂ = −1.
Can I find a perpendicular line equation given a point and another line?
Yes: find the perpendicular slope (−1/m), then use point-slope form: y − y₀ = m₂(x − x₀).
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