# Calculating the Midpoint - Problem 3

FREE It is also possible to use the midpoint formula to find one of the endpoints of the line segment, when given the other endpoint, (x_{1}, y_{1}). The goal is to find the other endpoint, (x_{2}, y_{2}). The midpoint formula states that you can find the midpoint (x, y) by finding the values of x = (x_{1} + x_{2})/2 and y = (y_{1} + y_{2})/2. Since you know the values of x_{1}, y_{1}, x, and y, it is possible to use algebra to solve for x_{2} and y_{2}. By manipulating the formula, you will find that x_{2} = 2x - x_{1}, and y_{2} = 2y - y_{1}. So, using this, you can plug in the known numbers to find the second endpoint.

Sometimes with midpoints you are going to be given a midpoint and asked to find one of the endpoints. It’s best if you draw a picture.

So here we know where our end point is. It’s at (-3,2) so again I’m going to go back to my x and y axis, x is horizontal y is vertical so that the end point is at (-3,2) so I’m going to make an E there for an endpoint. We know that midpoint is at 3 and -8 so I’m going to go over 3 and down 1 2 3 4 5 6 7 8 so I can say this is our midpoint, so I know that my other endpoint is going to be somewhere way down there in the forth quadrant.

So we also work backwards. Start by using our formula. The x coordinate is equal to the average of your two x order pairs. So you’ve got x1 plus x2 divided by 2. So we know what x is, this is your midpoint and that’s 3 and that’s going to equal x1, x1 is -3 plus x2 all divided by 2. So what we have to do here is solve for x2 since we know this end point right here is x2 and y2.

First step is undo division so I’m going to multiply both sides by 2. 2 times 3 is 6, so we have 6 equals -3 plus x2 and one step we can solve by adding 3 and I’ll move it a little bit down to the right and I see that 9 is equal to x2. So we are half way there how do we find our y coordinate by doing the same process.

We know that the y coordinate or midpoint is equal to the average of not our Xs but here we are talking about Ys. So I’m going to add up my Ys and divide by 2. But what is the y coordinate of the midpoint? Well the y coordinate of the midpoint we said it was -8. So -8 is equal to y1 which is

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