# Calculating the Midpoint - Problem 1

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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).

Applying what you know about the midpoint formula that is taking the average of two points to find halfway in between them let’s look at the specific problem. Here we are given two end points one at (-15,7) one at (3,9) and I’m asking you where is that mid point?

So let’s start by sketching a graph. We’ve got two axes an 'x' and a 'y' and always remember to label them and again I’m just going to sketch this I’m not going to write out 15 little hash marks. So I’m going to go -15 and up 7 and then for the other point I’m going to go over 3 and up 9. I know that this point has to be a little bit higher than that point and we can see that our midpoints are going to be somewhere I’m going to guess maybe in the second quadrant.

So let’s start by writing our formula x equals x1 plus x2 divided by 2. What you should notice is this looks just like an average and that’s all you are really doing. So x1 is -15 x2 is 3, so you have your formula you've identified your givens now substitute and solve.

X is going to equal -15 plus 3, all divided by 2. Now what your geometry teacher wants you to do is he wants to see all this work. If you make some little mistake in integer addition he’ll probably give you most if the credit or she. -15 plus 3 we know that is -12, -12 divided in half is -6. So we have one point we know that we are going to be adding -6, here so I’m just going to write that in -6. Now we have to find out what’s the y coordinate. So just like the Xs we are going to have to find the Ys. So I’m going to say our y is equal to y1 plus y2 all divided by 2.

Our y1 is 7 our y2 is 9, now it doesn’t really matter which one you pick for y1 or y2 because addition is commutative which means your adding doesn’t matter. So y is equal to 7 plus 9 divided by 2. Notice I picked nice even numbers so that we don’t get any decimals. I want you to make sure you understand the process and not necessarily can you divide decimals. 16 divide by 2 is 8 so we can see that our midpoint I’m going to write it nice and big is at (-6,8).

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