Is it possible to find the midpoint between any two points in the plane? That is, given two points \(\left( {{x_1},{y_1}} \right)\) and \(\left( {{x_2},{y_2}} \right)\), is it possible to find the point exactly halfway between those two points? The answer is yes! With the midpoint formula, we can find such a point. The midpoint works similarly to how we find *average* in mathematics. To find the average between two numbers, you add the numbers, and divide by two. The midpoint formula works similarly. Let’s give the formula, and then jump straight to an example.

**Definition:** The *midpoint* of the line segment with endpoints \(\left( {{x_1},{y_1}} \right)\) and \(\left( {{x_2},{y_2}} \right)\) is given by

\(\left( {\Large \frac{{{x_1} + {x_2}}}{2},\Large \frac{{{y_1} + {y_2}}}{2}} \right)\)

**Example:** Find the midpoint of the line segment with endpoints \(\left( { - 2.8,9.2} \right)\) and \(\left( { - 9.5, - 11.9} \right)\).

**Solution:** We use the midpoint formula. Here we have \({x_1} = - 2.8\), \({x_2} = - 9.5\), \({y_1} = 9.2\), and \({y_2} = - 11.9\). It’s as simple as plugging in the numbers. Then the midpoint of the line segment with the given endpoints is

\(\left( {\Large \frac{{{x_1} + {x_2}}}{2},\Large \frac{{{y_1} + {y_2}}}{2}} \right) = \left( {\Large \frac{{\left( { - 2.8} \right) + \left( { - 9.5} \right)}}{2},\Large \frac{{\left( {9.2} \right) + \left( { - 11.9} \right)}}{2}} \right)\)

\( = \left( {\Large \frac{{ - 12.3}}{2},\Large \Large \frac{{ - 2.7}}{2}} \right)\)

\( = \left( { - 6.15, - 1.35} \right)\)

Here is a figure illustrating what the midpoint looks like:

In the figure, you can see the two original endpoints of the segment, as well as the midpoint that we calculated. Visually you should be motivated to believe that \(\left( { - 6.15, - 1.35} \right)\) is indeed the midpoint of that line segment.

Let’s look at one more example. Find the midpoint of the line segment with endpoints \(\left( {9.7, - 7.6} \right)\) and \(\left( {4.1,7.9} \right)\).

Again we just label our values and plug them in. Here we have \({x_1} = 9.7\), \({x_2} = 4.1\), \({y_1} = - 7.6\) and \({y_2} = 7.9\). Plug these into the midpoint formula:

The midpoint of the line segment with the given endpoints is

\(\left( {\Large \frac{{{x_1} + {x_2}}}{2},\Large \frac{{{y_1} + {y_2}}}{2}} \right) = \left( {\Large \frac{{9.7 + 4.1}}{2},\Large \frac{{ - 7.6 + 7.9}}{2}} \right)\)

\( = \left( {\Large \frac{{13.8}}{2},\Large \frac{{0.3}}{2}} \right)\)

\( = \left( {6.9,0.15} \right)\)

Here is a figure illustrating our result:

Below you can **download** some** free** math worksheets and practice.

Find the midpoint of the line segment with the given endpoints.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Find the midpoint of the line segment with the given endpoints.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Given the midpoint and one endpoint of a line segment, find the other endpoint.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**