# GRE Math : Midpoint Formula

## Example Questions

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

There is a line defined by two end-points,  and .  The midpoint between these two points is .  What is the value of the point ?

Explanation:

Recall that to find the midpoint of two points  and , you use the equation:

.

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

You merely need to solve each coordinate for its respective value.

Then, for the y-coordinate:

Therefore, our other point is:

### Example Question #1 : Midpoint Formula

There is a line defined by two end-points,  and .  The midpoint between these two points is .  What is the value of the point ?

Explanation:

Recall that to find the midpoint of two points  and , you use the equation:

.

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

You merely need to solve each coordinate for its respective value.

Then, for the y-coordinate:

Therefore, our other point is:

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

What is the other endpoint of a line segment with one point that is  and a midpoint of ?

Explanation:

Recall that the midpoint formula is like finding the average of the  and  values for two points.  For two points  and , it is:

For our points, we are looking for .  We know:

We can solve for each of these coordinates separately:

X-Coordinate

Y-Coordinate:

Therefore, our point is

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

What is the other endpoint of a line segment with one point that is  and a midpoint of ?

Explanation:

What is the other endpoint of a line segment with one point that is  and a midpoint of ?

Recall that the midpoint formula is like finding the average of the  and  values for two points.  For two points  and , it is:

For our points, we are looking for .  We know:

We can solve for each of these coordinates separately:

X-Coordinate

Y-Coordinate:

Therefore, our point is

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

What is the midpoint of (2, 5) and (14, 18)?

(16, 23)

(–10, –13)

(7, 9)

(1, 2.5)

(8, 11.5)

(8, 11.5)

Explanation:

The midpoint between two given points is found by solving for the average of each of the correlative coordinates of the given points.  That is:

Midpoint = ( (2 + 14)/2 , (18 + 5)/2) = (16/2, 23/2) = (8, 11.5)

### Example Question #2 : How To Find The Midpoint Of A Line Segment

What is the midpoint between the points (1,3,7) and (–3,1,3)?

(5,2,4)

(3,1,2)

(2,–1,5)

(–1,2,5)

(2,2,5)

(–1,2,5)

Explanation:

To find the midpoint, we add up the corresponding coordinates and divide by 2.

[1 + –3] / 2 = –1

[3 + 1] / 2 = 2

[7 + 3] / 2 = 5

Then the midpoint is (–1,2,5).

### Example Question #71 : Coordinate Geometry

A line which cuts another line segment into two equal parts is called a ___________.

transversal

parallel line

midpoint

horizontal line

bisector

bisector

Explanation:

This is the definition of a bisector.

A midpoint is the point on a line that divides it into two equal parts. The bisector cuts the line at the midpoint, but the midpoint is not a line.

A transversal is a line that cuts across two or more lines that are usually parallel.

Parallel line and horizontal line don't make sense as answer choices here. The answer is bisector.

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