Midpoint Formula

Geometry · Axiom Academy

Find the point exactly halfway between two points on a coordinate plane. Start with two endpoints, A and B . The midpoint M is the one point on the segment that is the same distance from each — it splits AB into two equal halves. For endpoints (x_1, y_1) and (x_2, y_2) M is the average of the two endpoints The formula does the balancing one axis at a time: average the two x -values to get the midpoint's x, and average the two y -values to get its y. Add, then divide by 2 — that's it. The midpoint is the average of the x-coordinates and the average of the y-coordinates. Add both x's, divide by 2. Add both y's, divide by 2. Worked example: midpoint of A(2, 3) and B(8, 7) On a coordinate plane the result is easy to trust by eye. Plot A(1, 1) and B(7, 4) , draw the segment, and the midpoint lands at the center — equally far along each half of AB . To find any midpoint, you only need the two endpoints — no graph required. Average the x's, average the y's, and write the pair: (\, ,\ \,) . Try it on your own points and check that the answer always sits dead center. The midpoint formula is just the average position between two points — add and divide by 2 for each coordinate. Scroll up to revisit any step.

This is the written version of the interactive lesson above. See the full Geometry course.