A graph showing how to find the endpoint of a line segment on the Cartesian plane
Starting point coordinates
x₁
y₁
Midpoint coordinates
xM
yM
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Table of contents:

  1. Endpoint Calculator
  2. Endpoint Formula
  3. Find endpoint example

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

This Endpoint Calculator will find the missing endpoint from the midpoint and the known endpoint.

To find midpoint coordinates use Midpoint Calculator.

Endpoint Formula

If (x1, y1) are the coordinates of starting point, (xM, yM) are the coordinates of midpoint, then the coordinates of the endpoint (x2, y2) can be calculated by the formula:

x_{\tiny 2} = 2x_{\tiny M} – x_{\tiny 1}

y_{\tiny 2} = 2y_{\tiny M} – y_{\tiny 1}

Or shortly:

Endpoint(x_{\tiny 2},y_{\tiny 2}) = (2 x_{\tiny M} – x_{\tiny 1}, 2 y_{\tiny M} – y_{\tiny 1})

Find endpoint example

Find the endpoint of a line segment where we know one endpoint is (-3, -5) and the midpoint is (1, 2).

To answer what the endpoint of line segment is, simply replace the values in the formula to find the coordinates of the endpoint.

x_{\tiny 2} = 2 \cdot 1 – (-3) = 2 + 3 = 5

y_{\tiny 2} = 2 \cdot 2 – (-5) = 4 + 5 = 9

The endpoint of the line segment defined by coordinates of start point (-3, -5) and midpoint (1, 2) is (x2, y2) = (5, 9).

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