📐 Perpendicular Line Calculator
Calculate equation of a perpendicular line
Point on perpendicular line (x, y)
How to Use This Calculator
Enter Original Line Slope
Input the slope m of the original line.
Enter Point on Perpendicular Line
Input coordinates (x, y) of a point that the perpendicular line passes through.
Calculate
Press "Calculate Perpendicular Line" to find the equation of the perpendicular line.
Formula
Perpendicular lines have negative reciprocal slopes
m₂ = -1/m₁
y - y₁ = m₂(x - x₁) where m₂ = -1/m₁
Key Point: Perpendicular lines have slopes that are negative reciprocals. If the original slope is m, the perpendicular slope is -1/m. Exception: A horizontal line (m=0) is perpendicular to a vertical line.
Example: Original slope = 2, perpendicular slope = -1/2 = -0.5
About Perpendicular Line Calculator
The Perpendicular Line Calculator finds the equation of a line perpendicular to a given line passing through a specified point. Perpendicular lines intersect at right angles (90°).
When to Use This Calculator
- Geometry: Find perpendicular line equations
- Mathematics: Solve problems involving perpendicular lines
- Engineering: Design perpendicular structures
Frequently Asked Questions
What makes two lines perpendicular?
Two lines are perpendicular if they intersect at a right angle (90°). Their slopes are negative reciprocals: m₁ × m₂ = -1.
How do I find a perpendicular line?
Use the negative reciprocal of the original slope: m₂ = -1/m₁. Then use point-slope form: y - y₁ = m₂(x - x₁), where (x₁, y₁) is the point on the perpendicular line.
What if the original line is horizontal?
If m = 0 (horizontal line), the perpendicular line is vertical (undefined slope) with equation x = x₁, where (x₁, y₁) is the point on the perpendicular line.