Construct a line through a point using the negative reciprocal of a nonzero finite slope. Formula and perpendicular line remain visible in one place for independent verification.
Perpendicular construction supports normals, shortest-distance problems, right-angle geometry, and coordinate proofs.
Nonvertical perpendicular lines have slopes whose product is −1. The new point determines the intercept of the perpendicular line.
A line perpendicular to slope 2 has slope −1/2. Through (3,4), its intercept is 5.5, giving y=−0.5x+5.5. This Perpendicular Line example can be compared with parallel line.
Take −1/m, substitute the supplied point into b=y−m⊥x, and check that m×m⊥=−1.
An impossible perpendicular line sign or magnitude should prompt a Perpendicular Line input review before rounding.
Link Given nonzero slope to its Perpendicular Line role. Link New point x to its Perpendicular Line role. The retained Perpendicular Line formula identifies the Perpendicular Line model.
A horizontal source line has a vertical perpendicular and cannot be represented by finite slope-intercept form on this page. If the Perpendicular Line assumptions do not fit, consider source slope.
Substitute the Perpendicular Line solution into Given nonzero slope. This Perpendicular Line check rejects false Perpendicular Line branches and forbidden denominators.
Choose an easy Given nonzero slope value before running Perpendicular Line. Predict New point x, then compare it with the Perpendicular Line output.
The Perpendicular Line case starts with Given nonzero slope and New point x. Recalculate Perpendicular line from those entries. A nearby New point y can challenge the Perpendicular Line relationship, but its Perpendicular line belongs to a separate Perpendicular Line record.
A round value for Given nonzero slope gives Perpendicular Line a quick boundary test. Leave New point x fixed, predict Perpendicular line, and compare that prediction with the new Perpendicular Line output. A disagreement identifies a specific part of the Perpendicular Line setup to inspect.
It makes the slope product −1.
The perpendicular is vertical.
No; it anchors the new perpendicular line.
Yes, depending on the chosen point.