Endpoint Calculator

What is an Endpoint?

An endpoint in geometry is a point that identifies a section of a straight line. For example, a segment is uniquely defined by two points, A and B, with a single point that bisects it, such as M (middle point).

A line segment’s endpoint is any point at either end. A line in a line segment does not extend past its endpoints. It is therefore described as a point where a line finishes.

Endpoint Formula

To derive the endpoint from the midpoint and other endpoints, we can use this formula

\( x_2 = 2x – x_1 \)

\( y_2 = 2y – y_1 \)

Where,

• \( (x_2, y_2) \) are the coordinates of the endpoint
• \( (x_1, y_1) \) are the starting point coordinate
• (x, y) are the coordinates of the midpoint.

Endpoints and Midpoints

• Endpoints are the locations along a segment where a line terminates.
• Midpoints are the exact center of the line segment, located where the endpoints are.

The midpoint and the endpoint formula are connected. A midpoint is a location in the center of a line connecting two points. The midpoint formula can determine the other midpoint given one endpoint and a midpoint. Both midpoint and endpoint calculators are available on the internet for easy calculations.

Example

Example 1: Point A is (5, 7). Point B is (x, y). The midpoint of AB is (17, –4). Next, find the endpoints of the line segment.

Point A is (5, 7). Point B is (x, y). The midpoint of AB is (17, –4). What is the value of B?

We need to use the midpoint formula which is \( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \).

\( MP = ( \dfrac{5 + x}{2}, \dfrac{7 + y}{2} ) \)

Solving each of them separately, we get:

\( \dfrac{5 + x}{2} = 17 → 5 + x = 34 → x = 29 \)

\( \dfrac{7 + y}{2} = –4 → 7 + y = –8 → y = –15 \)

B is (29, –15).

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