Perpendicular Line Calculator

Your details

Choose how you will describe the original line.
The slope of the original line in y = mx + b.
The y-intercept of the original line.
The perpendicular line will pass through this point.
The perpendicular line will pass through this point.
Perpendicular slope
-0.5

Negative reciprocal of the original slope

Perpendicular line equationy = -0.5x + 2.5
Standard formx+2y - 5 = 0
Original line equationy = 2x + 1
Intersection x0.6
Intersection y2.2
Distance from P to line 12.6833
Original slope2
Original slope2
Perpendicular slope-0.5

Perpendicular line: y = -0.5x + 2.5

  • The original line has slope 2. Its perpendicular slope is the negative reciprocal: -0.5.
  • The two slopes multiply to -1, confirming the lines meet at a 90-degree angle.
  • The two lines intersect at the point (0.6, 2.2).
  • The shortest distance from point P to the original line is 2.6833 units, measured along the perpendicular.

Next stepTo confirm your answer, verify that the two slopes multiply to exactly -1, and that substituting the given point into your perpendicular equation gives the correct y-value.

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