Calculator
Results
Diagram
Teacher mode
Use Alt+S to copy a shareable URL and Alt+L to copy the LaTeX summary. Tip: use ArrowUp/ArrowDown to nudge numeric inputs (default step: 1; for m and r: 0.1; Shift ×10, Alt ×0.1, Ctrl/Cmd ×0.01).
How to use this coordinate geometry calculator
Choose the mode that matches your task, enter the required coordinates or coefficients, then compare the numeric result, algebraic form, and plotted diagram together. The page is most useful when you want to verify a classroom example, check a worked solution, or sanity-check a sketch before you share it.
Use it in 3 steps
- Pick one mode and start with the minimum required inputs only.
- Read the main result first, then check the diagram and step list to confirm the geometry matches your expectation.
- If you change an input, change only one value at a time so you can explain why the line, circle, or intersection moved.
What this page helps with
Use it for distance, midpoint, slope, line equations, perpendicular and parallel constructions, point-line distance, circles, circumcircles, and line-circle intersections. It is designed for fast browser-based checks with the algebra shown beside the graph.
Common mistakes to avoid
- Entering the same point twice when the formula requires two distinct points.
- Treating a vertical line as a numeric slope instead of using
verticalwhere supported. - Comparing standard form, slope-intercept form, and point-slope form without checking whether they represent the same line.
- Reusing rounded display values as if they were the exact internal values.
Worked example
For P₁ = (0, 0) and P₂ = (3, 4), the distance is 5, the midpoint is (1.5, 2), the slope is 4/3, and the line through both points is y = (4/3)x. Use that baseline to confirm the diagram, then switch to another mode such as point-line distance or circle-through-3-points to compare how the same coordinates behave in a new construction.
See also
Frequently asked questions
Which coordinate geometry formulas does this toolkit cover?
The calculator handles distance, midpoint, slope, two-point and point–slope lines, parallel and perpendicular lines through a point, perpendicular bisectors, point–line distance, line intersections, circles from center and radius or points, circumcircle of three points, and line–circle intersections.
How do I share the step-by-step working with students?
After computing a result, use the Copy shareable URL button or press Alt+S to generate a link with the inputs embedded. The Copy LaTeX button (Alt+L) exports the formulas for worksheets or handouts.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Why does this page differ from another tool?
Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.
How reliable are the displayed values?
Values are computed in the browser and rounded for display. They are good for planning and educational checks, but for regulated or high-stakes decisions you should validate assumptions with official guidance or professional review.