## anonymous one year ago Find the coordinates of the other endpoint if the midpoint is M(8, 2) and the other endpoint is P(5, 6). (6.5, 4) (21, 10) (11, -2) Help? Please

1. karatechopper

2. anonymous

I want to say midpoint but that's not right

3. karatechopper

It is right. :)

4. karatechopper

Okay. So you already know your midpoint. Do you realize that midpoint breaks into two separate parts in order to solve right? We solve for x, and then for y?

5. anonymous

Okay, so how do you break it into two parts?

6. karatechopper

Well let's do the x value first shall we? Midpoint formula looks like this: [(x_1 + x_2)/2 , (y_1 + y_2)/2] ----IN TOTAL But let's look at it in parts. To solve for Xm m=midpoint $\frac{ x1+x2 }{ 2 }$ That's x-value 1 and 2 btw. So I'll show you how to set up and how to find X-value we are looking for. Let's call the point we are looking for, x-value 1. and we know that the Xm is 8. Have you followed what I am saying so far?

7. anonymous

Yes

8. karatechopper

Great! So let's plug values in that we know. $\frac{ x1+5 }{ 2 }= 8$ --------I took the 5 from the x-value from point P and the 8 is the x-value from Midpoint.

9. karatechopper

Following?

10. anonymous

Okay, but how did you get 8?

11. karatechopper

Remember, Midpoint formula is used to find the midpoint. We were given the x-value of 8 as your midpoint in the question. We are using Midpoint formula in order to find your other point.

12. karatechopper

$\frac{ x1+x2 }{ 2 }=Xm$

13. anonymous

Oh right. Sorry I got confused

14. karatechopper

Refer to that if it helps you understand why I picked which points. :)

15. karatechopper

Alright so we can continue?

16. anonymous

17. karatechopper

Alright, now here's the part where I want to see if you can solve for the x-value by yourself. I set up the equation for you, now please solve for x1. I will check it for you. :) $\frac{ x1+5 }{ 2 }=8$

18. anonymous

Don't you first multiply everything by 2 to get rid of the fraction?

19. karatechopper

Correct.

20. anonymous

so is it x1+10=16? is that correct so far?

21. karatechopper

You don't multiply the 2 by the 5. When you multiple the 2 to get rid of the fraction then it cancels from the first side leaving you with only x1+5 and the other side being 16. Got it?

22. anonymous

Oh. okay, yes got it

23. anonymous

so x1=11

24. karatechopper

Good! Now can you set up the equation for y-value and try to solve that? It's the same steps in plugging and solving. Try it! :)

25. anonymous

So the answer is 11, -2?

26. karatechopper

Perfect!

27. karatechopper

Don't forget parenthesis

28. anonymous

Thank you :)

29. karatechopper

You are welcome. :D