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Endpoint Calculator

If you know one end of a line segment and its midpoint, the other end is fixed. Enter the known endpoint and the midpoint to get the missing endpoint and the full length of the segment.

Quick examples
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Missing endpoint(8, 11)
x₂
8
y₂
11
Length of the segment
10

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      Formula

      x₂ = 2 × midpoint x − x₁
      y₂ = 2 × midpoint y − y₁
      Segment length = 2 × distance from the known endpoint to the midpoint

      How to use it

      1. Enter the coordinates of the endpoint you know.
      2. Enter the coordinates of the midpoint.
      3. Read the missing endpoint.

      Worked examples

      One end at (2, 3) with the midpoint at (5, 7)

      Missing endpoint
      (8, 11)
      x₂
      8
      y₂
      11
      Length of the segment
      10

      One end at (−1, 4) with the midpoint at (2, −0.5)

      Missing endpoint
      (5, −5)
      x₂
      5
      y₂
      -5
      Length of the segment
      10.8167

      How it works

      The midpoint is the average of the two endpoints, so the missing end is as far beyond the midpoint as the known end is before it. From 2 to a midpoint of 5 is a step of 3; one more step of 3 lands on 8.

      Questions people ask

      What is the other endpoint if one is (2, 3) and the midpoint is (5, 7)?

      (2 × 5 − 2, 2 × 7 − 3) = (8, 11).

      Can the missing endpoint have negative coordinates?

      Yes. With an endpoint at (−1, 4) and a midpoint at (2, −0.5), the other endpoint is (5, −5).

      How is this different from the midpoint formula?

      It is the same formula solved backwards: instead of averaging two ends to get the middle, you use the middle and one end to recover the other.

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