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How to Determine the Length of a Segment When Knowing the Midpoint

A series of points connected together form a line segment; though not all of the segment's points are equal in importance. The three main points of a line segment are its endpoints, which define its beginning and ending, and its midpoint, which is the point that marks the segment's center. By knowing the line segment's midpoint and one of its endpoints, you can calculate the distance from the midpoint to the endpoint and then determine the segment's overall length.

Instructions

    • 1

      Subtract the midpoint's x-coordinate from the endpoint's x-coordinate, and then square the resulting difference. For an example, let the midpoint be (1, 3) and the endpoint be (5, 6). Subtracting 1 from 5, or 5 - 1, results in 4, and the square of 4 is 16.

    • 2

      Subtract the midpoint's y-coordinate from the same endpoint's y-coordinate, and then square the resulting difference. With this example, subtracting 3 from 6, or 6 - 3, results in 3, and the square of 3 is 9.

    • 3

      Sum the two squares, and then find the sum's square root for the distance between the midpoint and endpoint. In this example, 16 added to 9 equals 25, and the square root of 25 is 5.

    • 4

      Multiply the distance by 2 to determine the length of the line segment. Concluding this example, 5 multiplied by 2 equals 10 --- the length of the line segment is 10 units.

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