# SSAT Upper Level Math : How to find the endpoints of a line segment

## Example Questions

### Example Question #2072 : Hspt Mathematics

A line segment on the coordinate plane has midpoint . One of its endpoints is . What is the -coordinate of the other endpoint, in terms of  and/or ?

Explanation:

Let  be the -coordinate of the other endpoint. Since the -coordinate of the midpoint of the segment is the mean of those of the endpoints, we can set up an equation as follows:

### Example Question #1 : Midpoint Formula

A line segment on the coordinate plane has one endpoint at ; its midpoint is . Which of the following gives the -coordinate of its other endpoint in terms of  and  ?

Explanation:

To find the value of the -coordinate of the other endpoint, we will assign the variable . Then, since the -coordinate of the midpoint of the segment is the mean of those of its endpoints, the equation that we can set up is

.

We solve for :

### Example Question #11 : Midpoint Formula

One endpoint of a line segment on the coordinate plane is the point  ; the midpoint of the segment is the point . Give the -coordinate of the other endpoint of the segment.

Explanation:

In the  part of the midpoint formula

,

set , and solve:

This is the correct -coordinate.

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

One endpoint of a line segment on the coordinate plane is the point  ; the midpoint of the segment is the point . Give the -coordinate of the other endpoint of the segment.

Explanation:

Using the  part of the midpoint formula

set  and solve:

The second endpoint is .

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

On the coordinate plane,  is the midpoint of  and  is the midpoint of  has coordinates  and  has coordinates

Give the -coordinate of .

Explanation:

First, find the -coordinate of . In the  part of the midpoint formula

,

set , and solve:

Now, find the -coordinate of  similarly, setting

This is the correct response.

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

On the coordinate plane,  is the midpoint of  and  is the midpoint of  has coordinates  and  has coordinates

Give the -coordinate of .

Explanation:

First, find the -coordinate of . In the  part of the midpoint formula

,

set , and solve:

Now, find the -coordinate of  similarly, setting

This is the correct response.

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

On the coordinate plane,  is the midpoint of  and  is the midpoint of  has coordinates  and  has coordinates

Give the -coordinate of .

Explanation:

First, find the -coordinate of . In the  part of the midpoint formula

,

set , and solve:

Now, find the -coordinate of  similarly, setting

This is the correct response.

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

On the coordinate plane,  is the midpoint of  and  is the midpoint of  has coordinates  and  has coordinates

Give the -coordinate of .

Explanation:

First, find the -coordinate of . In the  part of the midpoint formula using the coordinates from  and

,

set , and solve:

Now, find the -coordinate of  similarly, setting

This is the correct response.