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Calculating the Midpoint - Concept
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).
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.