Endpoint Calculator

Use our endpoint calculator to find an endpoint of a line segment given the other endpoint and the midpoint.

Endpoint Coordinates:

(5, 5)

Line Graph:

Steps to Find the Endpoint

Start with the endpoint formula

\left( 2x_{m} - x_{1}, \space 2y_{m} - y_{1} \right )

Substitute the known point values in the formula and solve

\left( (2 \times 3) - 1, \space (2 \times 4) - 3 \right )

\left( 6 - 1, \space 8 - 3 \right )

\left( 5, \space 5 \right )

Learn how we calculated this below

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How to Find the Endpoint of a Line Segment

A line segment is defined by its endpoints, which are the points on either end of the line. A line segment is a line that connects two points, which are its endpoints.

If you know one endpoint, then you can find the other endpoint, but you’ll need some additional information. You will need to know the length of the line and its slope or the midpoint of the line segment.

Given one of the line segment’s endpoints and its midpoint, you can find the other endpoint using a simple formula.

Endpoint Formula

The formula to find the coordinates of the endpoint (x₂, y₂) of a line segment using the other endpoint (x₁, y₁) and the midpoint (x_m, y_m) is:

x_{2}=x_{m}+(x_{m}-x_{1})

y_{2}=y_{m}+(y_{m}-y_{1})

This can be simplified to:

x_{2}=2x_{m}-x_{1}

y_{2}=2y_{m}-y_{1}

Thus, the x-coordinate of the endpoint x₂ is equal to 2 times the x-coordinate of the midpoint x_m minus the x-coordinate of the other endpoint x₁. Similarly, the y-coordinate of the endpoint y₂ is equal to 2 times the y-coordinate of the midpoint y_m minus the y-coordinate of the other endpoint y₁.

So, the coordinates of the endpoint can be expressed as:

\left ( 2x_{m}-x_{1}, \space 2y_{m}-y_{1} \right )

Graphic showing the formula to calculate the missing endpoint of a line segment

You can find the midpoint to use in this formula with our midpoint calculator.

For example, let’s find the missing endpoint of a line segment with one endpoint (3, 5) and a midpoint (9, 7).

x_{2}=(2\times 9)-3=15

y_{2}=(2\times 7)-5=9

So, the missing endpoint of this line segment is (15, 9).

You may also be interested in our distance calculator to find the distance between the endpoints.