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In this lesson, you will become an expert on finding the point exactly in the middle between two points. This point is called the midpoint.

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. First, let's look at the midpoint on the number line. Use the Number Line applet below and collect some data.

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Use the following table to organize your information.

Click on the blanks to check your answers.

Point A	Point B	Midpoint C	Average of A & B
Interactive button. Assistance may be required. _____ -3.5	6.5	Interactive button. Assistance may be required. _____ 1.5	Interactive button. Assistance may be required. _____ 1.5
Interactive button. Assistance may be required. _____ -2.5	6.5	Interactive button. Assistance may be required. _____ 2	Interactive button. Assistance may be required. _____ 2
Interactive button. Assistance may be required. _____ -1	6.5	Interactive button. Assistance may be required. _____ 2.75	Interactive button. Assistance may be required. _____ 2.75
Interactive button. Assistance may be required. _____ -6.5	6.5	Interactive button. Assistance may be required. _____ 0	Interactive button. Assistance may be required. _____ 0

What did you notice about the midpoint's you found and the average of A & B?

Interactive popup. Assistance may be required.

Check Your Answer

They were the same.

So, the midpoint is just the average of the coordinate value?

How do you think that changes when you move to the coordinate plane?

Well, let’s find out.

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. Collect some data from the Midpoints on Grid applet. Use the following table to organize your information.

Use the following table to organize your information.

Click on the blanks to check your answers.

Point A	Point B	x(A)	x(B)	y(A)	y(B)	Average of x(A) and x(B)	Average of y(A) and y(B)	Midpoint
Interactive button. Assistance may be required. _____ (8,-1)	Interactive button. Assistance may be required. _____ (-2, 2)	Interactive button. Assistance may be required. _____ 8	Interactive button. Assistance may be required. _____ -2	Interactive button. Assistance may be required. _____ -1	Interactive button. Assistance may be required. _____ 2	Interactive button. Assistance may be required. _____ 3	Interactive button. Assistance may be required. _____ 0.5	Interactive button. Assistance may be required. _____ (3, 0.5)
Interactive button. Assistance may be required. _____ (4, 1)	Interactive button. Assistance may be required. _____ (1, -2)	Interactive button. Assistance may be required. _____ 4	Interactive button. Assistance may be required. _____ 1	Interactive button. Assistance may be required. _____ 1	Interactive button. Assistance may be required. _____ -2	Interactive button. Assistance may be required. _____ 2.5	Interactive button. Assistance may be required. _____ -0.5	Interactive button. Assistance may be required. _____ (2.5, -0.5)
Interactive button. Assistance may be required. _____ (6, 1)	Interactive button. Assistance may be required. _____ (-2, -1)	Interactive button. Assistance may be required. _____ 6	Interactive button. Assistance may be required. _____ -2	Interactive button. Assistance may be required. _____ 1	Interactive button. Assistance may be required. _____ -1	Interactive button. Assistance may be required. _____ 2	Interactive button. Assistance may be required. _____ 0	Interactive button. Assistance may be required. _____ (2,0)
Interactive button. Assistance may be required. _____ (2, -4)	Interactive button. Assistance may be required. _____ (1, 2)	Interactive button. Assistance may be required. _____ 2	Interactive button. Assistance may be required. _____ 1	Interactive button. Assistance may be required. _____ -4	Interactive button. Assistance may be required. _____ 2	Interactive button. Assistance may be required. _____ 1.5	Interactive button. Assistance may be required. _____ -1	Interactive button. Assistance may be required. _____ (1.5, -1)

How does the data you collected for midpoint compare to the data you collected for the average of the x-values and the average of the y-values?

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Check Your Answer

The coordinates for the midpoint are the same as the Average of the x-values and the Average of the y-values.

So it turns out that this is all there is to finding the midpoint; it's the average of the x's and the average of the y's from each endpoint.

The official formula looks like this:

M = ( x sub 1 plus x sub 2 all divided by 2 x₁ + x₂ 2 , y sub 1 plus y sub 2 all divided by 2 y₁ + y₂ 2 )

Note: capital M usually stands for midpoint, while lower case m is usually used for slope.