Endpoint Calculator

A line segment has two endpoints and a midpoint exactly halfway between them. In a Cartesian coordinate plane, the midpoint's x-coordinate is the average of the two endpoint x-coordinates, and its y-coordinate is the average of the endpoint y-coordinates. If one endpoint and the midpoint are known, those averaging equations can be rearranged to recover the other endpoint. The missing x-coordinate equals twice the midpoint x-coordinate minus the known x-coordinate. The missing y-coordinate follows the same pattern. This calculation works because the midpoint divides the segment into two equal directed displacements. Starting at the known endpoint, move to the midpoint by some horizontal and vertical amounts. Repeating that same displacement from the midpoint reaches the missing endpoint. The subtraction formula captures this reflection across the midpoint. It works in every quadrant and accepts negative, zero, decimal, or integer coordinates. No distance or slope calculation is needed because the two coordinate dimensions can be handled independently. Endpoint problems are common in coordinate geometry, analytic geometry, computer graphics, mapping, surveying, design, and vector applications. They can also appear as algebra exercises that require rearranging the midpoint formula. This calculator displays the recovered ordered pair and then averages it with the known endpoint as a check. That verification pair should reproduce the midpoint you entered. If it does, the result satisfies both coordinate equations. Displayed values are rounded to eight decimal places when necessary, while ordinary integer and short decimal answers remain easy to read. Be careful to match each x-coordinate with the x midpoint and each y-coordinate with the y midpoint. Coordinates are ordered, so swapping x and y changes the point. Also distinguish an endpoint from a segment length: this tool requires locations such as a point at two comma three, not the length between points. Both inputs must use the same coordinate scale and reference origin. In three dimensions the idea extends directly by applying the same formula to z, but this focused calculator handles the standard two-dimensional plane. You can verify visually by plotting all three points; the midpoint should lie on the segment and the two halves should have equal horizontal and vertical changes.