Question

The midpoint of line UV is (3, -11). The coordinates of one endpoint are U(3, 5). Find the coordinates of endpoint V.

Please help! Please just don't give me the answer. Explain to me step by step how to find the answer. Thanks! :)

Answer 1

Do you know how to find the average of two numbers?
For example, if you get a 100 and a 90 on two tests, what is your average test grade?

Answer 2

95?

Answer 3

Right.
Using the grades 100 and 90, how did you calculate the average?

Answer 4

By adding 100 and 90. Then dividing it by 2 because there are 2 numbers.

Answer 5

Am I correct?

Answer 6

Exactly.

Answer 7

Now that I know you understand how to find the average of two numbers, we can go on to your problem.

Answer 8

The midpoint of a segment has as coordinates the average of the x-coordinates and the average of the y-coordinates of the endpoints of the segment.

Answer 9

That may sound complicated, but it is very simple.

Answer 10

I think I understand. I tried it, and I got the answer -3

Answer 11

Let's say you have a segment with endpoints: A(0, 10) and B(4, 12).
To find the midpoint, all you need to do is find the average of the x-coordinates of the endpoints, and find the average of the y-coordinates of the endpoints.

The midpoint would be: x-coordinate: (0 + 4)/2 = 4/2 = 2
y-coordinate: (10 + 12)/2 = 22/2 = 11
The midpoint is M(2, 11)

Answer 12

Now you need to do this for your problem, but the difference is that you know what the average is. You need to find one point.

Answer 13

Oh okay. Let me try it one more time.

Answer 14

Is it (4, -3)?

Answer 15

So did I it wrong?

Answer 16

In your case, you have the midpoint and one endpoint. You need to find the other endpoint.

Answer 17

Yes, I think so.

Answer 18

So I added 5 + 3 = 8. Then I divided by 2 and that equals to 4. Next, I added -11 + 5. I got -6 and I divided it by 2 and I got -3. So I got (4, -3). What did I do wrong?