Midpoint Formula - How to use it

Midpoint Formula - How it Works - Video

Example 1

Example 1:

The midpoint formula is used to find the halfway point between two points. It is finding the average of two points.

Let's label (-4, 3) as the first point ==> (x_1, y₁) and let's label (2, 3) as the second point ==> (x_2, y₂). Our next step is to substitute the numbers into the formula ==> [(x₁ + x₂)/2, (y₁ + y₂)/2]

Let's start with substituting the x values

• ( -4 + 2)/2 Substitute x values, -4 for x₁ and 2 for x₂.

• -2/2 Add -4 and 2.

• -1 Divide -2 and 2.

Next let's substitute the y values

• ( 3 + 3)/2 Substitute x values, 3 for y₁ and 2 for y₂.

• 6/2 Add 3 and 3.

• 3 Divide 6 and 2.

Now we have our midpoint (-1, 3). If we count the spaces starting at point A to point M, it is 3 spaces. And if we continue from point M to point B, it is also 3 spaces. So our final answer for the midpoint is (-1, 3).

Example 2

Example 2:

The midpoint formula is used to find the halfway point between two points. It is finding the average of two points.

Let's label (2, 4) as the first point ==> (x_1, y₁) and let's label (2, -1) as the second point ==> (x_2, y₂). Our next step is to substitute the numbers into the formula ==> [(x₁ + x₂)/2, (y₁ + y₂)/2]

Let's start with substituting the x values

• ( 2 + 2)/2 Substitute x values, 2 for x₁ and 2 for x₂.

• 4/2 Add 2 and 2.

• 2 Divide 4 and 2.

Next let's substitute the y values

• ( 4 + -1)/2 Substitute x values, 4 for y₁ and -1 for y₂.

• 3/2 Add 4 and -1.

• 1.5 Divide 3 and 2.

Now we have our midpoint (2, 1.5). If we count the spaces starting at point B to point M, it is 2.5 spaces. And if we continue from point M to point A, it is also 2.5 spaces. So our final answer for the midpoint is (2, 1.5).

Example 3

Example 3:

The midpoint formula is used to find the halfway point between two points. It is finding the average of two points.

This time we are going to attack the problem a different way.

Let's count from point B vertically so that we reach the same line as point A. That is 4 spaces. Now we can draw a dotted line halfway toward segment AB.

Let's count from from where we stopped to point A. That is 8 spaces. Now we can draw a dotted line halfway toward segment AB. Where the two dotted lines meet is our midpoint.

To check we can use the midpoint formula.

Let's label (-3, 0) as the first point ==> (x_1, y₁) and let's label (5, 4) as the second point ==> (x_2, y₂). Our next step is to substitute the numbers into the formula ==> [(x₁ + x₂)/2, (y₁ + y₂)/2]

Let's start with substituting the x values

• ( -3 + 5)/2 Substitute x values, -3 for x₁ and 5 for x₂.

• 2/2 Add -3 and 5.

• 1 Divide 2 and 2.

Next let's substitute the y values

• ( 0 + 4)/2 Substitute x values, 0 for y₁ and 4 for y₂.

• 4/2 Add 0 and 4.

• 2 Divide 4 and 2.

Now we have our midpoint (1, 2). If we count the spaces starting at point A to point M, it is 3 spaces. And if we continue from point M to point B, it is also 3 spaces. So our final answer for the midpoint is (1, 2).

Live Worksheet

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