Midpoint Formula
In this lesson, the midpoint between two points whose coordinates are known will be found. We will also develop a general formula for determining the coordinates of the midpoint and go through several examples.
Suppose it is desired to find the midpoint between the points (1, 2) and (3, -2) shown on the grid below.

To do this, we first look at a number line and find the midpoint between x = 1 and x = 3.

The principle that we apply will give us a general formula for the midpoint between any two points with given coordinates. The point that is exactly halfway between 1 and 3 on this one-dimensional number line is 2. This can be found by averaging the 2 coordinates:

If we apply the averaging strategy to our two points, we have: x = .

Therefore, the midpoint between (1, 2) and (3, –2) is (2, 0).
The Midpoint Formula:
We can generalize the method used above. The midpoint between any two points is given by . This is known as “the midpoint formula.”
Let's practice:
1. What is the midpoint between the points (5, 6) and (– 12, 40)?
We apply the midpoint formula:
1. If the midpoint between (1, 4) and (x, 10) is (–4, 7), what is the value of x?
We apply the midpoint formula for the 1st coordinate: which gives us x = – 9.

Examples
 What is the midpoint between (–2, 7) and (4, 6)? What is your answer?
 If the midpoint between (x, 3) and (9, 14) is , what is the value of x? What is your answer?

M Ransom

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