# Intermediate Geometry : Midpoint Formula

## Example Questions

### Example Question #41 : Coordinate Geometry

A line with endpoints of  and  has a midpoint of . What are the coordinates of the unknown endpoint?

Explanation:

Recall how to find the midpoint of a line:

In other words, the coordinates of the midpoint are just the average of the  and  coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the  coordinate by using the given midpoint and endpoint.

Now, let's solve for the  coordinate.

The coordinate for the other endpoint must be .

### Example Question #42 : Coordinate Geometry

A line with endpoints of  and  has a midpoint of . What are the coordinates of the unknown endpoint?

Explanation:

Recall how to find the midpoint of a line:

In other words, the coordinates of the midpoint are just the average of the  and  coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the  coordinate by using the given midpoint and endpoint.

Now, let's solve for the  coordinate.

The coordinate for the other endpoint must be .

### Example Question #43 : Coordinate Geometry

A line segment has an endpoint at  and a midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #44 : Coordinate Geometry

A line segment has an endpoint at  and a midpoint at . Find the coordinates of the other midpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #45 : Coordinate Geometry

A line segment has an endpoint at  and a midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #46 : Coordinate Geometry

A line segment has an endpoint at  and midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #47 : Coordinate Geometry

A line segment has an endpoint at  and midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #48 : Coordinate Geometry

A line segment has an endpoint at  and midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #49 : Coordinate Geometry

A line segment has an endpoint at  and midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .

### Example Question #50 : Coordinate Geometry

A line segment has an endpoint at  and midpoint at . Find the coordinates of the other endpoint.

Explanation:

Recall how to find the midpoint of a line segment:

,

where  are the endpoints.

Let's first focus on the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

Solve for .

Next, find the  coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

The second endpoint must be at .