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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.

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  1. misty1212
    • one year ago
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    HI!!

  2. misty1212
    • one year ago
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    this looks hard, but i bet we can do it

  3. anonymous
    • one year ago
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    i totally dont get it lol

  4. misty1212
    • one year ago
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    yeah lets think for second and see what we can come up with

  5. imqwerty
    • one year ago
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    u have a formula to find this :)

  6. misty1212
    • one year ago
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    first off that means we are going to break it in to 6 equal parts, and take 5 of them

  7. misty1212
    • one year ago
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    |dw:1440470612550:dw|

  8. imqwerty
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    |dw:1440470712719:dw|

  11. anonymous
    • one year ago
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    so is 3/2 the answer?

  12. misty1212
    • one year ago
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    add \(5\times \frac{3}{2}\) to \(3\) and get \(10.5\)

  13. misty1212
    • one year ago
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    no the answer is not a number, it is a point

  14. misty1212
    • one year ago
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    the first coordinate of that point, if i am not mistaken, is \(10.5\)

  15. imqwerty
    • one year ago
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    No the answer is (21/2, 3) :)

  16. misty1212
    • one year ago
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    lol 21/2=10.5

  17. misty1212
    • one year ago
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    now we need the second coordinate

  18. anonymous
    • one year ago
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    so how did we get that again?

  19. misty1212
    • one year ago
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    which, according to @imqwerty is 3

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

  21. misty1212
    • one year ago
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    @imqwerty used a formula i don't know

  22. misty1212
    • one year ago
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    you want to use the formula?

  23. anonymous
    • one year ago
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    not really, i dont get it

  24. imqwerty
    • one year ago
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    that^ link has the proof :)

  25. misty1212
    • one year ago
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    so you want to do it without the formula?

  26. misty1212
    • one year ago
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    your choice

  27. anonymous
    • one year ago
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    nah

  28. misty1212
    • one year ago
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    ok lets go slow then

  29. misty1212
    • one year ago
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    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
    • one year ago
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    yea

  31. misty1212
    • one year ago
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    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
    • one year ago
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    the first coordinate of one point is 3, of the other is 12 it is clear that they are 9 units apart?

  33. anonymous
    • one year ago
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    yup

  34. misty1212
    • one year ago
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    then we break that in to 6 pieces, so each will have length \(\frac{9}{6}\) or \(\frac{3}{2}\)

  35. misty1212
    • one year ago
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    so far so good?

  36. anonymous
    • one year ago
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    yes

  37. misty1212
    • one year ago
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    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
    • one year ago
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    i get \[3+5\times 1.5=10.5\] as the first coordinate

  39. misty1212
    • one year ago
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    now we can repeat with the second coordinates

  40. anonymous
    • one year ago
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    okay

  41. misty1212
    • one year ago
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    which is easier since they will be whole numbers

  42. misty1212
    • one year ago
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    from -1 to 5 is 6 units right?

  43. misty1212
    • one year ago
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    break that up in to 6 pieces each has length 1 since \(\frac{6}{6}=1\)

  44. misty1212
    • one year ago
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    again we want to add five of those to \(-1\) so \(-1+5=4\)

  45. misty1212
    • one year ago
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    answer:\[(10.5,4)\]

  46. misty1212
    • one year ago
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    hmm not the same answer as @imqwerty got, but i am going to stick with that one

  47. anonymous
    • one year ago
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    okay thanks for all your help

  48. misty1212
    • one year ago
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    \[\color\magenta\heartsuit\]

  49. imqwerty
    • one year ago
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    wait no

  50. misty1212
    • one year ago
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    we can do it the formula way if you like see if we get the same answer

  51. imqwerty
    • one year ago
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    24/6=4 sry for the mistake the answer is (10.5, 4)

  52. imqwerty
    • one year ago
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    :)

  53. misty1212
    • one year ago
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    i actually have never seen that formula thanks!

  54. imqwerty
    • one year ago
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    welcome :)

  55. misty1212
    • one year ago
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    \[\left(\frac{5\times 12+3}{6}, \frac{5\times 5-1}{6}\right)\]

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