Perpendicular Line Calculator | Find Equation & Slope
Easily calculate the equation of a perpendicular line with our online calculator. Enter a point and the slope of a given line to find the perpendicular slope and equation. Perfect for geometry and math problem-solving.
Enter Line Details
Result:
Point of Intersection:
Understanding Perpendicular Lines
In geometry, perpendicular lines are lines that intersect at a right angle (90 degrees). If two lines are perpendicular, the product of their slopes is -1, unless one line is vertical (undefined slope) and the other is horizontal (slope of 0).
Formula for Perpendicular Slope
If a line has a slope \( m \), the slope of a line perpendicular to it, \( m_{\perp} \), is given by:
Point-Slope Form
The equation of a line can be expressed in point-slope form as:
Where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. Using this, we can find the equation of the perpendicular line. This calculator helps you find the equation of such a perpendicular line and its intersection point with the original line (if y-intercept is provided for the original line).