# Calculating the Midpoint - Problem 2

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You can find the midpoint of a line segment if given the coordinates of its endpoints by using the midpoint formula. The endpoints of the line segment are given by (x_{1}, y_{1}) and (x_{2}, y_{2}). To find the x-coordinate of the midpoint, use the formula: x = (x_{1} + x_{2})/2. To find the y-coordinate, use the same formula, but this time, using the y-coordinates of the endpoints: y = (y_{1} + y_{2})/2. Putting these two results together, the midpoint is of the line segment is at (x, y).

A segment and a coordinate plane sometimes you might get a decimal. So let’s take a look at an example. Here we have points at (5,-2) and (-8,1). Like a good geometry student I’m going to draw a picture first just so I have an idea of what is a reasonable answer.

So 5 and -2 I’m going to go over 5 and down 2 so that’s going to be my first point, my next points are at -8 and +1. So if I connect those two I see in the midpoints it might be somewhere on the second quadrant or the third quadrant but not quite sure where.

So if our midpoint is at (x,y) so I’m saying that this point here that I circle is at x and y, being calculated by taking the average of your Xs, average of your Ys so x1 plus x2 divided by 2 and our x's is 5 and -8. So x equals 5 plus -8 divide by 2, 5 and -8 is -3 divided by 2, and if you want to you can convert that to a decimal by saying that’s -1.5.

So I’m going to erase this x and I know that our x coordinate is -1.5. Do the same thing to find your Ys. Y is equal to the average of your 2y coordinates. We have -2 and +1, so y is equal to -2 plus 1 divided by 2. -2 and 1 is -1 divided by 2 and -1/2 we can write as a decimal as -0.5. So erase the y and we know that this is -0.5 and we draw a box on it to tell our teacher that that’s our answer. Our midpoint is at -1.5 and -0.5 which happens to be in our third quadrant.

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