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anonymous

  • one year ago

find the distance from the line 4x+3y=5 to the point (6,9)

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  1. anonymous
    • one year ago
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    distance equation?

  2. anonymous
    • one year ago
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    m=-4/3 y-9=-4/3(x-6) y-9=-4/3x+8 y=-4/3x +17 (0, 5/3) and (6,9) d=s.rt (6-0)^2+(9-5/3)^2 =9.47511

  3. anonymous
    • one year ago
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    perhaps try this.

  4. anonymous
    • one year ago
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    The distance from a point P(x,o,yo) to a line ax+by+c = 0 is \[d=\frac{ \left| ax _{o}+by _{o}+c \right| }{ \sqrt{a^2+b^2} }\]

  5. anonymous
    • one year ago
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    \[d=\frac{ \left| 4(6)+3(9)-5 \right| }{ \sqrt{4^2+3^2} }\]

  6. anonymous
    • one year ago
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    been a while since I've done this so please correct me if i'm wrong

  7. anonymous
    • one year ago
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    i got 9.2... but the hint say first find the line through the point (6,9) parallel to the given line, and then find the distance between these lines

  8. welshfella
    • one year ago
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    you made a slight error on the slope of the line perpendicular to the given line its slope is - 1 / (-4/3) = 3/4

  9. welshfella
    • one year ago
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    - oh the parallel line ! sorry

  10. anonymous
    • one year ago
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    so was it right or wrong?

  11. welshfella
    • one year ago
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    chrs00's method is correct and that comes to 9.2

  12. anonymous
    • one year ago
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    yep

  13. welshfella
    • one year ago
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    why did you use (0,5/3) on the original line?

  14. anonymous
    • one year ago
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    i think he just used any point on that line. i think you need to use a point that is perpendicular to that line

  15. anonymous
    • one year ago
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    distance=shortest distance

  16. anonymous
    • one year ago
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    are u sure ..this question is structure different frm the previous set of questions that i did..they want .. to find distance frm the point (a,b) eg.(4,8) to the line y=sumthing eg 6x+8y=9 ... inwhich i used that formula provide by chrs00 but the question ask to find the distance frm the line given to the point given...

  17. welshfella
    • one year ago
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    Chris00 formula gives you just that

  18. anonymous
    • one year ago
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    you were given a point that did not lie on that line

  19. welshfella
    • one year ago
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    another way to do it is to find the equation of the line perpendicular to the original line and passing through the point (6,9) then solving the 2 equations simultaneously to find the point of intersection. Then use the distance formula with this point and (6,9) But that's a bit long-winded.

  20. anonymous
    • one year ago
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    ok

  21. anonymous
    • one year ago
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    can u sketch it?

  22. welshfella
    • one year ago
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    you can sketch it on the desmos web site

  23. anonymous
    • one year ago
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    but i wouldnt get desmos to use in my test

  24. welshfella
    • one year ago
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    the 2 parallel lines will look something like |dw:1444387746919:dw|

  25. anonymous
    • one year ago
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    ok

  26. welshfella
    • one year ago
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    the line joining the point (0, 5/3) and (6,9) is not perpendicular to the 2 parallel lines. That is why you didn't get the right answer

  27. anonymous
    • one year ago
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    |dw:1444384572508:dw|

  28. welshfella
    • one year ago
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    yea - did they give you that point (0. 5/3)?

  29. anonymous
    • one year ago
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    no

  30. anonymous
    • one year ago
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    i get that from the equation 4x+3y=5

  31. welshfella
    • one year ago
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    yes i see Well you cant take any old point . The line joining the point to (6,9) must be perpendicular ( shortest distance)

  32. anonymous
    • one year ago
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    ok

  33. anonymous
    • one year ago
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    thank you both

  34. anonymous
    • one year ago
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    : )

  35. welshfella
    • one year ago
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    the formula that chris00 used is the easiest way to do it. Finding the line perpendicular etc ( the way i mentined) is long and messy yw

  36. anonymous
    • one year ago
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    good luck in your studies

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