Midpoint ⇒ x

If you are studying geometry and need to calculate the endpoint of a segment, you have entered the right website. The endpoint calculator that we present here will allow you to find the endpoint from the midpoint and from another endpoint. You will get detailed solutions step by step and with graphical representation, which makes it an ideal study tool.

To use the endpoint calculator follow these steps:

- Enter the coordinates of the known endpoint.
- Enter the coordinates of the midpoint.
- Press the green button “Calculate end point”, doing so will show the solution explained step by step next to the graphic solution.

Endpoints are the two points that delimit a line segment. An example is shown in the following image:

In geometry, an endpoint is a point at the end of a line segment or curve. A line segment is a portion of a line that has two endpoints, and a curve is a continuous, smooth path that may or may not have endpoints, depending on the specific type of curve.

For example, a straight line is a line segment that has two endpoints, while a circle is a curve that has no endpoints. A ray is a line segment that has one endpoint and extends indefinitely in one direction, while an arc is a portion of a curve that has two endpoints.

Endpoints are used to define the length and direction of a line segment or curve, and they play an important role in various geometric concepts and calculations, such as distance, slope, and angle measures.

If we know the midpoint (x_{m}, y_{m}) and the endpoint (x_{1}, y_{1}) of a line segment, we can calculate the coordinates of the missing endpoint (x_{2}, y_{2}) by applying the endpoint formula:

(x, _{2}y) = (2 (_{2}x) – _{m}x, 2 (_{1}y) – _{m}y)_{1} |

We show you how to calculate the missing endpoint using the following examples:

**Example 01: The diameter of a circle forms a line segment that has an endpoint at coordinates (5, 3). Knowing that the center of the circle is at coordinates (0, 0), find the missing endpoint of the line segment.**

- The center of the circle is the midpoint of the line segment, so (x
_{m}, y_{m}) = (0, 0). - The coordinates of the known end point are (x
_{1}, y_{1}) = (5, 3).

Now we apply the endpoint formula to find the coordinates of the missing endpoint:

x_{2} = 2 (*x _{m}*) –

x_{2} = 2 (0) – *5*

x_{2} = – *5*

_{y2} = 2 (y* _{m}*) – y

_{y2} = 2 (0) – 3

_{y2} = – 3

**Missing endpoint: (-5,-3)**

**Example 02: Find the missing endpoint of a segment with a midpoint at coordinates (-3.8, 6.3) and an endpoint at coordinates (-7.2, 9.6).**

Known values:

- (x
_{m}, y_{m}) = (-3.8, 6.3). - (x
_{1}, y_{1}) = (-7.2, 9.6).

Now we calculate the coordinates of the missing endpoint using the endpoint formula:

x_{2} = 2 (*x _{m}*) –

x_{2} = 2 (-3.8) – (-7.2)

x_{2} = 0.4

_{y2} = 2 (y* _{m}*) – y

_{y2} = 2 (6.3) – 9.6

_{y2} = 3

**Missing endpoint: (0.4, 3)**