Endpoint calculator

Type the endpoint you know first and the midpoint second, such as A(1, 2) and M(5/2, 5). The other endpoint B appears as you type, with each coordinate worked out and a check that the midpoint of A and B really is M.

Whole numbers, decimals, fractions and mixed numbers all work, and six numbers give two points in 3D. Set Find back to the midpoint to go the other way, or use the midpoint calculator.

The midpoint is halfway, so B is as far past M as M is past A. For each coordinate, double the midpoint and take away the endpoint you know: x₂ = 2xₘ − x₁ and y₂ = 2yₘ − y₁.

With A(1, 2) and M(5/2, 5): x₂ = 2 × 5/2 − 1 = 4 and y₂ = 2 × 5 − 2 = 8, so B is (4, 8). Check it with the midpoint formula: (1 + 4) ÷ 2 = 5/2 and (2 + 8) ÷ 2 = 5, which is M.

This comes straight from the midpoint formula. xₘ = (x₁ + x₂)/2, so 2xₘ = x₁ + x₂, and taking x₁ from both sides leaves x₂.

On graph paper you can count instead. Count the steps across and up from A to M, then take the same steps again from M. From (−3, 4) to M(1, −1) is 4 right and 5 down; another 4 right and 5 down lands on B(5, −6).