# Intermediate Geometry : Midpoint Formula

## Example Questions

### Example Question #31 : Coordinate Geometry

The midpoint for a line with an endpoint at  is . What are the coordinates for the other 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 #1 : How To Find The Endpoints Of A Line Segment

A line with the endpoints  and  has a midpoint at . What are the coordinates for 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 #33 : Coordinate Geometry

A line with endpoints at  and  has a midpoint of . What are the coordinates for 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 #34 : Coordinate Geometry

A line with endpoints at  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 #31 : Coordinate Geometry

A line with endpoints  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 #31 : 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 #31 : Midpoint Formula

A line with endpoints  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 #11 : How To Find The Endpoints Of A Line Segment

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 #12 : How To Find The Endpoints Of A Line Segment

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 #13 : How To Find The Endpoints Of A Line Segment

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 .