## anonymous one year ago PLEASE HELP!!!! A point H on a segment with endpoints B(3, −1) and Z(12, 5) partitions the segment in a 5:1 ratio. Find H. You must show all work to receive credit.

1. misty1212

HI!!

2. misty1212

this looks hard, but i bet we can do it

3. anonymous

i totally dont get it lol

4. misty1212

yeah lets think for second and see what we can come up with

5. imqwerty

u have a formula to find this :)

6. misty1212

first off that means we are going to break it in to 6 equal parts, and take 5 of them

7. misty1212

|dw:1440470612550:dw|

8. imqwerty

the cordinates of point P(x,y) which lies on segment AB with end points A(a,b) and B(c,d) and divides it in the ration m:n so u have - x=(mc+na)/(m+n) and y=(md+nb)/(m+n)

9. misty1212

yeah i don't get that formula from 3 to 12 is 9 units one sixth of that is $$\frac{9}{3}=\frac{3}{2}$$

10. imqwerty

|dw:1440470712719:dw|

11. anonymous

12. misty1212

add $$5\times \frac{3}{2}$$ to $$3$$ and get $$10.5$$

13. misty1212

no the answer is not a number, it is a point

14. misty1212

the first coordinate of that point, if i am not mistaken, is $$10.5$$

15. imqwerty

No the answer is (21/2, 3) :)

16. misty1212

lol 21/2=10.5

17. misty1212

now we need the second coordinate

18. anonymous

so how did we get that again?

19. misty1212

which, according to @imqwerty is 3

20. imqwerty

@misty1212 u can go here to see the proof of formula - http://kea.kar.nic.in/vikasana/bridge/maths/chap_13.pdf :)

21. misty1212

@imqwerty used a formula i don't know

22. misty1212

you want to use the formula?

23. anonymous

not really, i dont get it

24. imqwerty

that^ link has the proof :)

25. misty1212

so you want to do it without the formula?

26. misty1212

27. anonymous

nah

28. misty1212

ok lets go slow then

29. misty1212

first off, is it clear that if you want to break it in to a ratio that is 5:1 that is the same as dividing it up in to six parts, and taking five of them?

30. anonymous

yea

31. misty1212

ok so we are going to first break it in to six parts, then count out five we have to do it twice, once for each coordinate

32. misty1212

the first coordinate of one point is 3, of the other is 12 it is clear that they are 9 units apart?

33. anonymous

yup

34. misty1212

then we break that in to 6 pieces, so each will have length $$\frac{9}{6}$$ or $$\frac{3}{2}$$

35. misty1212

so far so good?

36. anonymous

yes

37. misty1212

ok now we want five of those, so staring at 3 we will add $$5\times \frac{3}{2}$$ or if you prefer $$5\times 1.5$$

38. misty1212

i get $3+5\times 1.5=10.5$ as the first coordinate

39. misty1212

now we can repeat with the second coordinates

40. anonymous

okay

41. misty1212

which is easier since they will be whole numbers

42. misty1212

from -1 to 5 is 6 units right?

43. misty1212

break that up in to 6 pieces each has length 1 since $$\frac{6}{6}=1$$

44. misty1212

again we want to add five of those to $$-1$$ so $$-1+5=4$$

45. misty1212

answer:$(10.5,4)$

46. misty1212

hmm not the same answer as @imqwerty got, but i am going to stick with that one

47. anonymous

okay thanks for all your help

48. misty1212

$\color\magenta\heartsuit$

49. imqwerty

wait no

50. misty1212

we can do it the formula way if you like see if we get the same answer

51. imqwerty

24/6=4 sry for the mistake the answer is (10.5, 4)

52. imqwerty

:)

53. misty1212

i actually have never seen that formula thanks!

54. imqwerty

welcome :)

55. misty1212

$\left(\frac{5\times 12+3}{6}, \frac{5\times 5-1}{6}\right)$