Free · Coordinate geometry calculators 📈

Perpendicular Line Through a Point & Intersection

Find the finite-slope perpendicular through a supplied point and its intersection with the original line.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

For y = 2x + 1 and point (2, 3), the perpendicular is y = −0.5x + 4. The two lines intersect at (1.2, 3.4).

Perpendicular slope = −1/m; its intercept = point y + point x/m

Enter these known values and leave the other values blank.

Both lines are represented in finite slope-intercept form. Their slopes must be nonzero; a horizontal/vertical pair needs a different representation.
Coordinates and intercepts may be signed or zero. Perpendicularity assumes equally scaled Cartesian axes and the usual Euclidean geometry.
The supplied point lies on the new perpendicular line and need not lie on the original line. Intersection coordinates are distinct from the supplied point unless it lies on both.

Its perpendicular is vertical, of the form x = a constant. A vertical line has no finite slope and is outside this slope-intercept calculator.

No. The calculator constructs a perpendicular through that point and then finds where it meets the original line.

Bookify requires nonzero slopes in this finite slope-intercept perpendicular-line model.