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Coordinate Geometry Toolkit — with steps

Explore distance, midpoint, slope, line and circle equations, and intersections. Every calculation shows the algebraic steps alongside a live coordinate plane diagram.

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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).

Worked example: P1 = (0, 0), P2 = (3, 4)

Use this pair as a quick first-paint check before the runtime result, diagram, and step list update. 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.

P1(0, 0)
P2(3, 4)
Distance5
Midpoint(1.5, 2)
Slope4/3
Line through both pointsy = (4/3)x

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

  1. Pick one mode and start with the minimum required inputs only.
  2. Read the main result first, then check the diagram and step list to confirm the geometry matches your expectation.
  3. 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

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 enter first for coordinate geometry?

Enter the point coordinates or line parameters for the object you want to measure. Keep the coordinate system fixed before comparing distance, midpoint, slope, or line equations.

Why can coordinate geometry results differ from nearby tools?

Differences usually come from coordinate order, signs, axis convention, and selected geometry operation. Match those assumptions before comparing this result with another CalcBE page, spreadsheet, or external tool.

How should I judge the reliability of the result?

Use the displayed result as reliable for the stated coordinate order, signs, axis convention, and selected geometry operation. For official reporting, regulated work, or purchasing decisions, verify the inputs against the source document or provider rule you must follow.