Free · Algebra and geometric relations

Recover Triangle Vertices from Three Midpoints

Find the original triangle vertices from all three side midpoints.

Calculator inputs

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

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For the worked example, x = 0, y = 0, x = 4, y = 0, x = 0, y = 6.

A=M₁+M₃−M₂; B=M₁+M₂−M₃; C=M₂+M₃−M₁

Enter these known values and leave the other values blank.

The three input points represent AB, BC and CA midpoints in that order.
All coordinates share one scale and origin. Collinear midpoints describe a degenerate triangle.

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

Bookify validates the real geometric or algebraic domain and inverse branches omitted or approximated by this capture.