Find the midpoint of a line segment, or work backwards to find the missing endpoint.
How midpoint is worked out
The midpoint is simply the average of the coordinates: average the x-values, average the y-values. The calculator also returns the distance, slope and the equation of the line through the two points, since those usually come up in the same question.
The reverse mode solves the more interesting version of the problem: given one endpoint and the midpoint, where is the other end?
How to fill it in
- Choose midpoint mode or endpoint mode.
- Enter the two points.
- Read the midpoint, distance, slope and line equation.
Formula reference
midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
endpoint = (2·xₘ − x₁, 2·yₘ − y₁)
The default scenario, worked through
Worked through, a mode of Find the midpoint from two points produces a midpoint of (5, 7). Underneath, Distance between the points comes out at 10 and Slope at 1.333333. Change any field and every figure updates as you type.
FAQ
How do I find the midpoint?
Average the two x-coordinates and average the two y-coordinates. That is the whole formula.
Can I find the other endpoint?
Yes — switch to endpoint mode, enter one end and the midpoint, and the calculator solves for the far end.
Does this work in three dimensions?
The same averaging works for a z-coordinate, though this tool covers the two-dimensional case.