# Intermediate Geometry : Midpoint Formula

## Example Questions

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### Example Question #1 : Coordinate Geometry

What is the midpoint between and ?

Explanation:

The midpoint is given by taking the mean, or average, of the and coordinates separately.

Let  and

So the midpoint formula becomes  and

So the midpoint is

### Example Question #2 : Coordinate Geometry

What is the midpoint of a line segment connecting the points  and

Explanation:

Use the midpoint formula:

### Example Question #3 : Coordinate Geometry

Given two points  and  and a line segment that connects the two.

What is the midpoint of the line segment? Addtionally, what is the length of the line segment?

Midpoint:

Length:

Midpoint:

Length:

Midpoint:

Length:

Midpoint:

Length:

Midpoint:

Length:

Midpoint:

Length:

Explanation:

The midpoint formula is as follows:

This makes sense; it is as simple as the average of the  and  components of each point.

For this problem, .

So the midpoint is

The distance formula is as follows:

The order you put the first and second components of each point does NOT matter, when a positive or negative number is squared, it will always come out positive.

So the distance is

### Example Question #4 : Coordinate Geometry

Find the midpoint of a line segment going from  to .

Explanation:

To find the midpoint of a line segment, you must find the mean of the x values and the mean of the y values.

Our x values are  and  to find their mean, we do .

Our y values are  and , so our mean is . Therefore, our midpoint must be .

### Example Question #5 : Coordinate Geometry

Find the coordinate of the midpoint of the line segment connecting the pair of points

and .

Cannot be determined

Explanation:

The coordinate of the midpoint of the line segment connecting a pair of points is

So for the pair of points  and ,

we get:

### Example Question #6 : Coordinate Geometry

Find the coordinate of the midpoint of the line segment connecting the pair of points

and .

Cannot be determined

Explanation:

The coordinate of the midpoint of the line segment connecting a pair of points is

.

So for the pair of points  and

we get,

### Example Question #7 : Coordinate Geometry

A line extends from the origin to . What is its midpoint?

Explanation:

The origin is the point . We can use the regular midpoint formula with as  and the given point  as :

Note that since the first point is the origin, we're averaging these points with 0, or in other words just dividing by 2.

### Example Question #8 : Coordinate Geometry

There is a line segment between the two points (5, 10) and (3, 6).  What formula will give you the correct mid-point of the line segment?

Explanation:

To find the mid-point given two points on the coordinate plane you are basically finding the average of the x-values and the average of the y-values.  To do this follow the formula below:

With our points this gives:

### Example Question #9 : Coordinate Geometry

A line has endpoints at (4,5) and (-6,8). Where is its midpoint?

Explanation:

The midpoint is the point that is equidistant from each endpoint point.

We find it using a formula that computes the average of the x and y coordinates.

### Example Question #10 : Coordinate Geometry

A line segment has the endpoints  and . What is the midpoint of this line segment?