Solve perpendicular slopes from gradients, points, equations. Review steps, compare intercepts, and visualize line behavior. Download polished summaries for classes, practice, reports, and revision.
| Scenario | Input | Original Slope | Perpendicular Slope | Perpendicular Line Through Point |
|---|---|---|---|---|
| Known slope | m = 2, point (3, -1) | 2 | -1/2 | y = -0.5x + 0.5 |
| Two points | (-2, 3) and (4, -1) | -2/3 | 3/2 | Through Point 1: y = 1.5x + 6 |
| Horizontal line | m = 0, point (5, 4) | 0 | Undefined | x = 5 |
| Vertical line | x = 7 | Undefined | 0 | y = 2 through point (1, 2) |
Main rule: For a nonzero slope m, the perpendicular slope is m⊥ = -1 / m.
Horizontal case: If m = 0, the perpendicular line is vertical, so its slope is undefined.
Vertical case: If the original line is vertical, the perpendicular line is horizontal, so its slope is 0.
From two points: m = (y2 - y1) / (x2 - x1), provided x2 ≠ x1.
From standard form: For Ax + By + C = 0, slope m = -A / B when B ≠ 0.
It is the negative reciprocal of the original slope when that slope is nonzero. Horizontal lines become vertical, and vertical lines become horizontal.
A vertical line has no finite slope because its run is zero. Dividing by zero is impossible, so the slope is reported as undefined.
Yes. Negative numbers, positive numbers, decimals, and fractions are supported. That makes the calculator useful for many classroom and exam-style problems.
Use the difference in y-values divided by the difference in x-values. After that, apply the negative reciprocal rule to get the perpendicular slope.
A zero slope means the original line is horizontal. The perpendicular line must be vertical, so its slope is undefined rather than numeric.
Slope alone gives the direction of a line, not its position. A point lets the calculator build the exact perpendicular equation and graph.
Yes. It converts Ax + By + C = 0 into slope information first, then calculates the perpendicular slope and the new line through your chosen point.
Yes. The graph shows the original and perpendicular lines together, so you can visually confirm the right-angle relationship and line position.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.