# Intermediate Geometry : Midpoint Formula

## Example Questions

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### Example Question #51 : Midpoint Formula

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 #52 : Midpoint Formula

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 #53 : Midpoint Formula

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 #54 : Midpoint Formula

A line segment has an endpoint at  and a midpoint at . Find 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 #55 : Midpoint Formula

A line segment on the coordinate plane has an endpoint at ; its midpoint is at .

True or false: Its other endpoint is located at .

False

True

True

Explanation:

The midpoint of a line segment with endpoints  and  is located at .

Therefore, set

and

In the first equation, set   and solve for :

Multiply both sides by 2:

Subtract 3.8 from both sides:

In the second equation, set   and solve for :

Multiply both sides by 2: