Enter your starting point (x1, y1) and midpoint (xm, ym) to find the missing endpoint of a line segment. The Endpoint Calculator applies the endpoint formula — (2xm − x1, 2ym − y1) — and returns the endpoint coordinates (x2, y2) along with a visual line graph breakdown.
Missing Endpoint (x2, y2)
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x₂ (Endpoint x)
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y₂ (Endpoint y)
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Line Segment Length
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Midpoint Verification
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To find the missing endpoint, use the endpoint formula: x2 = 2·xm − x1 and y2 = 2·ym − y1. Substitute the known endpoint coordinates (x1, y1) and the midpoint coordinates (xm, ym) into these equations and solve. This works because the midpoint is exactly halfway between the two endpoints.
The endpoint formula is derived from the midpoint formula. Since the midpoint M = ((x1 + x2)/2, (y1 + y2)/2), solving for the unknown endpoint gives: x2 = 2·xm − x1 and y2 = 2·ym − y1. This calculator applies this formula automatically once you enter the known values.
Using the endpoint formula: x2 = 2(3) − 1 = 5 and y2 = 2(5) − 3 = 7. So the missing endpoint is (5, 7). You can verify this by checking that the midpoint of (1, 3) and (5, 7) is indeed (3, 5).
Yes — this is possible if the line segment has zero length, meaning both endpoints are the same point. In that case, the midpoint coincides with both endpoints. Mathematically, if the midpoint equals the known endpoint (x1, y1), then the unknown endpoint (x2, y2) will also equal (x1, y1).
Once you know both endpoints (x1, y1) and (x2, y2), use the distance formula: d = √((x2 − x1)² + (y2 − y1)²). This calculator automatically computes the segment length for you after finding the missing endpoint.
Absolutely. The endpoint formula works for any real numbers — positive, negative, zero, or decimal. Simply enter your values in the input fields and the calculator handles the arithmetic, including negative and fractional coordinates.
An endpoint is one of the two defining points at either end of a line segment. A midpoint is the point that lies exactly halfway between the two endpoints, at equal distances from each. Given one endpoint and the midpoint, you can always find the other endpoint using the endpoint formula.
To verify, plug both endpoints back into the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). If the result matches the midpoint you originally entered, your answer is correct. This calculator displays a midpoint verification output so you can confirm accuracy immediately.