Find a line perpendicular to Ax + By + C = 0 through a point
Result
Perpendicular Line
Step-by-Step Derivation
Perpendicular Line Formula
Bx - Ay + C₂ = 0
A perpendicular line has a direction at a right angle to the original line. In standard form, swapping A and B and changing one sign gives a perpendicular coefficient pair.
⚠A and B should not both be zero. The point is substituted to determine the new constant.
How Perpendicular Lines Work
Perpendicular lines meet at a 90-degree angle. The new line uses coefficients that create a negative reciprocal slope compared with the original line.
Right Angle
Perpendicular lines meet at 90 degrees.
Coefficient Swap
Use B and -A for the new line.
New Constant
C2 makes the line pass through the point.
Slope Check
Slopes multiply to -1 when both exist.
💡 Example: For 2x+3y-5=0 through (3,2), use 3x-2y-5=0.
Applications of Perpendicular Lines Through a Point
Geometry ProofsNormal LinesConstructionGraphing
Frequently Asked Questions
What is a perpendicular line through point calculator?▼
It finds the line through a given point that is perpendicular to a given line.
What is the perpendicular line formula?▼
For Ax+By+C=0, one perpendicular standard-form line can use Bx-Ay+C2=0.
How do I use this calculator?▼
Enter A, B, C and the point coordinates, then click Calculate.
Why are the coefficients swapped?▼
Swapping A and B with a sign change creates a direction perpendicular to the original line.
Where are perpendicular lines used?▼
They are used in geometry proofs, construction, normal lines, and coordinate graphing.
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