Find the missing endpoint of a line segment from its midpoint and the other endpoint, with a midpoint check.
other endpoint
How to use this tool
Type the x and y coordinates of the midpoint of the line segment.
Type the x and y coordinates of one endpoint of the segment.
The calculator mirrors the known endpoint through the midpoint to find the missing one.
The recomputed midpoint from both endpoints is shown — it must match the midpoint you entered.
Formula & worked example
Midpoint (5, 5) and known endpoint (2, 3) give the other endpoint (8, 7), since 2 × 5 − 2 = 8 and 2 × 5 − 3 = 7. The segment length is √(36 + 16) = 7.2111.
Limitations — read this before you rely on it
This is plane (2D) coordinate geometry only. It assumes the given point really is the midpoint of the segment; if it is not, the answer is still the point that would make it the midpoint, which may not be what you intended. For 3D segments, apply the same formula to the z-coordinate as well.
Frequently asked questions
If M is the midpoint and one endpoint is (x₁, y₁), the other endpoint is (2Mₓ − x₁, 2Mᵧ − y₁). It mirrors the known endpoint through the midpoint.
Double the midpoint coordinates and subtract the known endpoint: midpoint (5, 5) and endpoint (2, 3) give (8, 7).
The midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2) — the average of the coordinates.
Only for a zero-length segment (both endpoints the same point). Otherwise the midpoint lies strictly between the two endpoints.
Yes — the formula is pure arithmetic and works in all four quadrants.