Perpendicular Line Calculator

Calculate perpendicular lines, slopes, and find equations of perpendicular lines.

Original Line (from two points)

Point for Perpendicular Line

Line Equations

Original Line:

y = 0.5000x + 0.0000

Perpendicular Line:

y = -2.0000x + 10.0000

Original Slope

0.5000

Perpendicular Slope

-2.0000

Perpendicular slope = -1 / original slope (negative reciprocal)

Line Properties

Angle Between Lines90 (perpendicular)
Distance to Original Line2.2361
Intersection Point(4.0000, 2.0000)
Product of Slopes-1.0000 (should be -1)

Perpendicular Verification

For perpendicular lines:

m1 * m2 = -1

0.5000 * -2.0000 = -1.0000

Lines are perpendicular!

Perpendicular Line Formulas

Perpendicular Slope

m_perp = -1 / m_original

The perpendicular slope is the negative reciprocal of the original slope.

Perpendicular Line Equation

y - y1 = m_perp(x - x1)

Point-slope form using the perpendicular slope and a given point.