Perpendicular Line Calculator

Find the equation of a perpendicular line passing through a given point and perpendicular to a line with a known slope.

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:

$$ m_{\perp} = -\frac{1}{m} $$

Point-Slope Form

The equation of a line can be expressed in point-slope form as:

$$ y - y_1 = m(x - x_1) $$

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).

Further Resources