## anonymous one year ago The midpoint of UV is (5,-11). One of the coordinates are U(3,5). Find V

1. freckles

$\text{ the midpoint of the line segment from point } (a,b) \text{ \to } (c,d) \text{ is } \\ (\frac{a+c}{2},\frac{b+d}{2})$

2. freckles

you are given: $\frac{3+c}{2} =5 \text{ and } \frac{5+d}{2}=-11$

3. freckles

where (c,d) is point V

4. anonymous

Would I have to plug something into the formula? How would the end result look

5. freckles

do you know how to solve equations yet?

6. freckles

maybe not... I guess since you are asking how to solve (3+c)/2=5 and also solve (5+d)/2=-11

7. freckles

the first I would do would be to multiply both sides by 2

8. freckles

for both equations

9. anonymous

Ok so that would give 5+d=-22?

10. freckles

yes for the second equation you have d+5=-22

11. anonymous

and then 3+c=10

12. freckles

do you the +5 on the side with d on it you are going to minus 5 on both sides because you know 5-5=0 so you will have d by itself

13. freckles

and that is right for the first equation so far

14. anonymous

And then you do the same to the other one too?

15. freckles

well not subtract 5 on both sides but subtract 3 on both sides yes

16. anonymous

So d=-27 and c=7?

17. freckles

ok great now remember (c,d) is the point V so your answer would be (7,-27) is the other endpoint V

18. freckles

so the midpoint of (7,-27) and (3,5) is $(\frac{3+7}{2},\frac{-27+5}{2})=(\frac{10}{2},\frac{-22}{2})=(5,-11)$

19. anonymous

Ok great I get it now

20. freckles

cool stuff have a good day :)

21. anonymous

Thank you very much for your help! My sister doesn't know how to do this, thank you

22. freckles

well go teach her then

23. anonymous

Ok i will now