Find Perpendicular Lines With Confidence
A perpendicular line meets another line at a right angle. This calculator helps you build that line from common classroom inputs. You can enter a slope and intercept. You can also enter two points. A standard form option is included for advanced work. The tool then finds the negative reciprocal slope, handles vertical cases, and writes the answer in several useful formats.
Why The Result Matters
Perpendicular lines appear in geometry, coordinate proofs, engineering sketches, graph design, and analytic problems. A single wrong sign can change the answer completely. This page shows the original slope, the perpendicular slope, the chosen point, and the final equation. It also displays point-slope, slope-intercept, and standard form when those forms are possible.
Formula Used
For a nonvertical and nonhorizontal line, the perpendicular slope is found with m2 = -1 / m1. Here m1 is the slope of the original line. The new line must pass through the point (x, y). Use b = y - m2x to find the intercept. The final equation is y = m2x + b. If the original line is vertical, the perpendicular line is horizontal. If the original line is horizontal, the perpendicular line is vertical. These special cases keep the right angle correct.
How To Use This Calculator
First, choose the input method. Use slope-intercept when you already know m and b. Use two points when the original line is defined by coordinates. Use standard form when the line is written as Ax + By + C = 0. Next, enter the point through which the perpendicular line should pass. Press calculate. The answer appears above the form, so you can review it before changing values.
Practical Notes
Use decimals when fractions are not convenient. Keep enough digits for accurate results. The table and export buttons help save your work. The CSV file is useful for spreadsheets. The PDF file is helpful for printing solutions. Always check whether the original line is vertical or horizontal, because those cases use simple direct equations.
Accuracy Tips
Round only after the final step. Store copied results with their input values. This makes review easier. When graphing, plot the shared point first. Then use the perpendicular slope to mark a second point on the new line.