Free · Coordinate geometry calculators 📈

Planar Segment Midpoint and Missing Endpoint Coordinate

Yes. Each coordinate is the arithmetic mean of the two endpoint coordinates on that axis. A negative position is valid; all axes must use a common coordinate scale.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: x₁ -2, y₁ 1, x₂ 4, y₂ 5 gives x midpoint 1, y midpoint 3.

M = ((x₁+x₂)/2, (y₁+y₂)/2)

Worked example

Enter these known values and leave the other values blank.

x₁
-2
y₁
1
x₂
4
y₂
5
x midpoint
1
y midpoint
3

Assumptions and limitations

  • All six Cartesian coordinates are editable and signed, with one common coordinate scale. The two axes solve independently. Two endpoint coordinates on an axis find their midpoint coordinate; a midpoint and either endpoint recover the other endpoint. Coincident endpoints are allowed. No physical length units are assigned to these coordinates.
  • Clear unknowns before solving backward and select compatible units. Original reference drawings do not scale to entered values. Independently rounded boundary measurements can be incompatible at finite precision.

Common questions

Can midpoint coordinates be negative?

Yes. Each coordinate is the arithmetic mean of the two endpoint coordinates on that axis. A negative position is valid; all axes must use a common coordinate scale.

How many measurements are needed?

Each axis requires either its two endpoint coordinates, or a midpoint coordinate and one endpoint. The x and y equations are independent.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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