# SAT II Math I : Midpoint Formula

## Example Questions

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### Example Question #1 : Midpoint Formula

Find the midpoint of the line that passes through the points and .

Explanation:

Recall the midpoint formula as .

Thus,

### Example Question #1 : Midpoint Formula

Find the midpoint of the line that passes through the points  and .

Explanation:

Recall the midpoint formula as .

Thus,

### Example Question #3 : Midpoint Formula

What is the midpoint between  and ?

Explanation:

The formula to find the midpoint is as follows:

In our case our

our

substituting in these values we get

midpoint =

### Example Question #1 : Midpoint Formula

What is the midpoint between  and ?

Explanation:

To find the midpoint of two points you find the average of both the  values and    values.

For

.

For

.

This means the midpoint is .

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

What is the midpoint of the points (3,12) and (9,15)?

Explanation:

To find the midpoint we must know the midpoint formula which is

We then take the -coordinate from the first point and plug it into the formula as .

We take the -coordinate from the second point and plug it into the formula as .

We then do the same for  and .

With all of the points plugged in our equation will look like this.

We then perform the necessary addition and division to get the answer of

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

Find the midpoint of the line segment that connects the two points below.

Point 1:

Point 2:

Explanation:

The average of the the -coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points.

, where  is and  is .

### Example Question #1 : Midpoint Formula

Find the midpoint of the line segment with endpoints  and .

Explanation:

Use the midpoint formula:

Substitute:

The midpoint is

### Example Question #6 : Midpoint Formula

Find the midpoint of the line segment with these endpoints:  and .

Explanation:

The midpoint formula is

.

Add the two  values together and divide the total by two to find the  value of the midpoint. Add the two  values together and divide the total by two to find the  value of the midpoint.

### Example Question #7 : Midpoint Formula

What is the midpoint of a line that connects the points  and ?

Explanation:

The midpoint formula is .

Therefore, all we need to do is plug in the points given to us to find the midpoint.

In this case, .

To find the -value for the midpoint, we add: . Then we divide by : .

To find the -value for the midpoint, we add: . Then we divide by : .

So our solution is .

### Example Question #8 : Midpoint Formula

Find the midpoint of a line with the endpoings (3, 4) and (-1, -1).

Explanation:

When finding the midpoint between two points, we use the midpoint formula

where  and  are the points given.

Knowing this, we can substitute the values into the formula.  We get

Therefore,  is the midpoint.

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