Retas Perpendiculares?
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
perp ⇔ m₁m₂=−1
About this calculator
This calculator checks whether two lines are perpendicular in the Cartesian plane. Two lines are perpendicular when the product of their slopes (m₁ and m₂) equals -1. The tool allows you to input the equations of the lines in slope-intercept form (y = mx + b) or general form (ax + by + c = 0), automatically calculates the slopes, and displays the result.
The operation is straightforward: the calculator extracts the slopes from the provided lines. In slope-intercept form, m is the coefficient of x. In general form, m = -a/b (with b ≠ 0). It then multiplies the two values and checks if the product equals -1 (with tolerance for rounding errors). If so, the lines are perpendicular; otherwise, they are not.
Use this calculator in situations such as: verifying if two streets on a map are perpendicular, checking geometry exercises, designing structures that require right angles (like squares or corners), or simply validating manual calculations. It is useful for students, teachers, and professionals in fields like engineering and architecture.
Important precautions: the calculator does not work for vertical lines (undefined slope), as perpendicularity in that case is verified by another criterion (a vertical line is perpendicular to a horizontal line). Also, ensure the equations are in the correct format and that denominators are not zero. The tool assumes the lines are distinct and not coincident.
Frequently asked questions
What does it mean for two lines to be perpendicular?
Two lines are perpendicular when they intersect at a 90-degree angle. In the Cartesian plane, this occurs when the product of their slopes equals -1.
How do I input a vertical line?
Vertical lines have equations like x = k and undefined slope. This calculator does not support vertical lines directly. To check perpendicularity with a vertical line, use another tool or remember: a vertical line is perpendicular to any horizontal line.
Does the calculator account for rounding errors?
Yes, the calculator uses a tolerance to compare the product with -1, avoiding false negatives due to rounding. The exact value may not be -1 but close enough.
Can I use this calculator for lines in 3D?
No, this tool is only for lines in the Cartesian plane (2D). For lines in three-dimensional space, perpendicularity involves direction vectors and dot product.
What if the lines are coincident?
Coincident lines are not perpendicular unless they are special lines (like the axes). The calculator may indicate they are not perpendicular, but check if the equations represent the same line.