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ineedyouubiebs

  • 2 years ago

What's a formula to uncover a way to divide a line segment into three equal parts. What would the formula look like?

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  1. ineedyouubiebs
    • 2 years ago
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    @some_someone ?

  2. ineedyouubiebs
    • 2 years ago
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    @satellite73 ?

  3. ineedyouubiebs
    • 2 years ago
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    @Luigi0210 lol sorry to bother you! /.\

  4. ineedyouubiebs
    • 2 years ago
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    Any clues at all?

  5. Luigi0210
    • 2 years ago
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    Nope, sorry :/

  6. ineedyouubiebs
    • 2 years ago
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    oh its fine I can try asking someone else:)

  7. ineedyouubiebs
    • 2 years ago
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    @dan815

  8. jim_thompson5910
    • 2 years ago
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    do you mean find the length of each piece? or actually trisect the segment through a geometric construction?

  9. ineedyouubiebs
    • 2 years ago
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    I think to find the length of each piece. The exact questions says: Now that you know how to find the midpoint from two endpoints, tweak your understanding of the formula to uncover a way to divide a line segment in to three equal parts. What would the formula look like?

  10. jim_thompson5910
    • 2 years ago
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    One way to do it is to divide the horizontal component of the length by 3 this will give you how far to space the points out in a horizontal sense you must do the same for the vertical component as well

  11. jim_thompson5910
    • 2 years ago
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    so say you had this segment |dw:1378786046754:dw|

  12. jim_thompson5910
    • 2 years ago
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    draw in the horizontal and vertical components |dw:1378786083004:dw|

  13. jim_thompson5910
    • 2 years ago
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    then cut those lengths into 3 congruent pieces |dw:1378786121773:dw|

  14. jim_thompson5910
    • 2 years ago
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    then use these cuts to figure out where the 1/3 and 2/3 markers go on the original line segment |dw:1378786176000:dw|

  15. jim_thompson5910
    • 2 years ago
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    |dw:1378786217033:dw|

  16. ineedyouubiebs
    • 2 years ago
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    yeah, i get what your saying, but there isn't any specific formula where you have to plug in the numbers?

  17. jim_thompson5910
    • 2 years ago
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    well this distance here |dw:1378786360035:dw| is the difference in the x coordinates

  18. jim_thompson5910
    • 2 years ago
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    this distance is the difference in the y coordinates |dw:1378786383951:dw|

  19. jim_thompson5910
    • 2 years ago
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    so you're subtracting the coordinates, then dividing by 3 to get those markers on the horizontal/vertical components and you're using those markers to get the 1/3 and 2/3 markers

  20. ineedyouubiebs
    • 2 years ago
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    but the question is asking me for a formula?

  21. jim_thompson5910
    • 2 years ago
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    I know, I'm trying to get you to think of what that formula would be based on what I'm giving you

  22. ineedyouubiebs
    • 2 years ago
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    Ahhh okay

  23. ineedyouubiebs
    • 2 years ago
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    how about a+b+c=? divide by 3

  24. jim_thompson5910
    • 2 years ago
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    not quite

  25. jim_thompson5910
    • 2 years ago
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    remember you're taking the differences in the corresponding coordinates, then dividing by 3

  26. ineedyouubiebs
    • 2 years ago
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    oh so then instead of adding them, im subtracting them?

  27. jim_thompson5910
    • 2 years ago
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    let m = |x2 - x1| this is the horizontal component length and let n = |y2 - y1| this is the vertical component length

  28. jim_thompson5910
    • 2 years ago
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    cut these distances into 3rds: m ---> m/3 n ---> n/3 so if you have the segment with the endpoints (x1,y1) and (x2,y2), then you're adding on m/3 to the coordinates to get these points 1/3 marker: (x1 + 1*m/3, y1 + 1*n/3) 2/3 marker: (x1 + 2*m/3, y1 + 2*n/3) you could avoid using m and n and just use the distances above, but that notation gets even uglier

  29. ineedyouubiebs
    • 2 years ago
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    yeah, this looks really complicated lol:p

  30. jim_thompson5910
    • 2 years ago
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    it's not too bad once you get used to it

  31. ineedyouubiebs
    • 2 years ago
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    thanks for helping me tough. i hope the teacher goes over this tommorow because right now i just want to know out!

  32. jim_thompson5910
    • 2 years ago
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    do you see how I defined m and n?

  33. ineedyouubiebs
    • 2 years ago
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    Yeah, yes I did:)

  34. jim_thompson5910
    • 2 years ago
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    so if you cut m into 3 then you basically get this distance here |dw:1378787464289:dw|

  35. jim_thompson5910
    • 2 years ago
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    and if you divide n by 3, you get this length here |dw:1378787503944:dw|

  36. jim_thompson5910
    • 2 years ago
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    with me so far?

  37. ineedyouubiebs
    • 2 years ago
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    yes, with you so far:)

  38. jim_thompson5910
    • 2 years ago
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    so that's why if you start with (x1,y1) |dw:1378787643610:dw|

  39. jim_thompson5910
    • 2 years ago
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    and you move m/3 units along the x axis and n/3 units along the y axis, then you'll land at the 1/3 marker |dw:1378787687368:dw|

  40. jim_thompson5910
    • 2 years ago
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    that explains why the coordinate of the 1/3 marker is (x1 + m/3, y1 + n/3) and you can write it as (x1 + 1*m/3, y1 + 1*n/3)

  41. ineedyouubiebs
    • 2 years ago
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    thank you so much i appreciate it:)

  42. jim_thompson5910
    • 2 years ago
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    you're welcome, the 2/3 mark is found in much the same way, you add on another m/3 to the x coordinate and another n/3 to the y coordinate to get 2/3 marker: (x1 + m/3+m/3, y1 + n/3+n/3) which turns into 2/3 marker: (x1 + 2*m/3, y1 + 2*n/3)

  43. dan815
    • 2 years ago
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    |dw:1378813283291:dw|

  44. dan815
    • 2 years ago
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    |dw:1378813443142:dw|

  45. dan815
    • 2 years ago
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    jims way is the nicest way though

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