Finding the Midpoint
By using x and y coordinates, it is easy to find the midpoint of a line segment. Finding the midpoint is calculated by taking the average of the x coordinates and then taking the average of the y coordinates. For example, if we had two coordinates located at (1,3) and (5, 7) our midpoint would be (3, 5).
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If we apply what we know about the midpoint of this line segment to a coordinate plane, that is using x's and y's we can come up with a formula that will calculate the midpoint of any line segment that we can come up with. So here I have x1, y1 those 1s do not mean that we're multiplying x by 1, they don't mean we're raising it to the first power they're just a name. They're saying the first point x coordinate, first point y coordinate. Same thing with x2 and y2.
So to find the midpoint which we said, divides a line segment in half, what we're going to do is we're going to take the average of our x's. So x1+x2 since I have two terms I'm going to divide that by 2. That's a definition of an average, so by adding together the x's and dividing in half I can find the x coordinate. Do the same thing for the y's, y1+y2 divided by 2 will give us the y coordinate of our midpoint.
