# Intermediate Geometry : How to find the endpoints of a line segment

## Example Questions

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

What is the midpoint between the two points:

and

Explanation:

The midpoint formula is

If we plug in our points we get

### Example Question #3 : 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 #4 : How To Find The Endpoints Of A Line Segment

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

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 #6 : 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

### Example Question #7 : How To Find The Endpoints Of A Line Segment

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 #8 : 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 #9 : How To Find The Endpoints Of A Line Segment

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

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 .

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