GED Math : Midpoint Formula

Example Questions

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Example Question #1 : Midpoint Formula

Find the midpoint of the line segment that connects the following points:

Explanation:

Use the midpoint formula:

Example Question #2 : Midpoint Formula

You are given  and  is the midpoint of  is the midpoint of . What are the coordinates of  ?

Explanation:

Repeated application of the midpoint formula  yields the following:

Since  is the midpoint of , substitute the coordinates of  for  and , set equal to the coordinates of , and solve as follows:

is the point .

We can find the coordinates of  similarly using those of  and :

is the point

Example Question #3 : Midpoint Formula

You are given points  and .  is the midpoint of  is the midpoint of , and  is the midpoint of . Give the coordinates of .

Explanation:

Repeated application of the midpoint formula, , yields the following:

is the point  and  is the point  is the midpoint of , so  has coordinates

, or .

is the midpoint of , so  has coordinates

, or .

is the midpoint of , so  has coordinates

, or .

Example Question #4 : Midpoint Formula

What is the midpoint between  and ?

Explanation:

Write the formula to find the midpoint.

Substitute the points into the equation.

The midpoint is located at:

Example Question #5 : Midpoint Formula

Find the midpoint of  and .

Explanation:

Write the formula for the midpoint.

Substitute the points.

Example Question #6 : Midpoint Formula

What is the midpoint between  and ?

Explanation:

Recall that the general formula for the midpoint between two points is:

Think of this like being the "average" of your two points.

Based on your data, you know that your midpoint could be calculated as follows:

This is the same as:

Example Question #7 : Midpoint Formula

What is the midpoint between the points  and ?

Explanation:

Recall that the general formula for the midpoint between two points is:

Think of this like being the "average" of your two points.

Based on your data, you know that your midpoint could be calculated as follows:

This is the same as:

Example Question #8 : Midpoint Formula

is the midpoint between  and some other point.  What is that point?

Explanation:

Recall that the general formula for the midpoint between two points is:

Think of this like being the "average" of your two points.

Now, you can write your data out as follows, as you know the midpoint value as well as one of the values for your end points:

To finish solving, think of it like two different equations:

and

Now, solve each for the respective values:

and

Therefore, your other point is  or

Example Question #9 : Midpoint Formula

is the midpoint between  and some other point.  What is that point?

Explanation:

Recall that the general formula for the midpoint between two points is:

Think of this like being the "average" of your two points.

Now, you can write your data out as follows, as you know the midpoint value as well as one of the values for your end points:

To finish solving, think of it like two different equations:

and

Now, solve each for the respective values:

and

Therefore, your other point is  or

Example Question #10 : Midpoint Formula

Find the midpoint of the following points:

Explanation:

To find the midpoint between two points, we will use the following formula:

where  and  are the given points.

So, given the points

and , we can substitute into the formula. We get

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