# Intermediate Geometry : Midpoint Formula

## Example Questions

### Example Question #1301 : Intermediate Geometry

Find the midpoint of a line segment that has endpoints at  and .

Explanation:

Recall the formula for finding a midpoint of a line segment:

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

### Example Question #1302 : Intermediate Geometry

Find the midpoint of a line segment that has endpoints at  and .

Explanation:

Recall how to find the midpoint of a line segment with endpoints at  and :

### Example Question #21 : Lines

Find the midpoint of a line segment that has endpoints at  and .

Explanation:

Recall how to find the midpoint of a line segment with endpoints at  and :

### Example Question #22 : Coordinate Geometry

A line segment on the coordinate plane has its endpoints at  and .

True or false: Its midpoint is located at .

True

False

False

Explanation:

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

Set , and evaluate both expressions:

The midpoint is at , so the statement is false.

### Example Question #1 : How To Find The Endpoints Of A Line Segment

Find the midpoint between the points:

and

Explanation:

The midpoint formula is

So for our two points the equation is

### Example Question #21 : Coordinate Geometry

What is the midpoint between the two points:

and

Explanation:

The midpoint formula is

If we plug in our points we get

### Example Question #1 : How To Find The Endpoints Of A Line Segment

What is the midpoint between the two points:

and

Explanation:

The midpoint formula is

So lets plug in our two points, that gives us

### Example Question #28 : Coordinate Geometry

What is the midpoint between the two points:

and

Explanation:

The equation to find the midpoint between two points is

If we plug in our values of the two points we get

### Example Question #22 : Midpoint Formula

One of the endpoints of a line is and the midpoint is . What is the other endpoint?

Explanation:

The midpoint's coordinates are the average of the endpoints'.

This means that the x-coordinates of the two endpoints have a mean of 1:

multiply both sides by 2

subtract 8

this means the other endpoint's x-coordinate is -6

This also means that the y-coordinates of the two endpoints have a mean of -3:

multiply both sides by 2

The coordinate pair that we're looking for is (-6, 1)

### Example Question #1 : How To Find The Endpoints Of A Line Segment

The midpoint of a line is and one of the endpoints is . What is the other endpoint?

Explanation:

The midpoint's coordinates are just the mean of the endpoints'.

This means that the mean of the two x-coordinates is 9:

multiply both sides by 2

subtract 1

This also means that the mean of the two y-coordinates is 9:

multiply both sides by 2

subtract 17

So the other endpoint we were solving for is