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davian Group Title

J is the midpoint of The coordinates of J are (-8,7) and the coordinates of K are (3,4) find the coordinates of L. can someone help me? i get really confused with geometry and im trying to finish this final and im not sure how to solve this problem

  • 2 years ago
  • 2 years ago

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  1. across Group Title
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    I think your description is incomplete, but I get the idea. Okay, let's look at it this way: |dw:1324417543699:dw|

    • 2 years ago
  2. across Group Title
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    J is supposed to be the midpoint of the line |LK|, and we know both its coordinates and the coordinates of point K.

    • 2 years ago
  3. davian Group Title
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    oh sorry yea its suppose to be J is the midpoint of KL

    • 2 years ago
  4. across Group Title
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    A good way to tackle this would be to find the equation of the line formed by the points J and K, that is, find the equation of the line |JK|. Do you know how to do that?

    • 2 years ago
  5. davian Group Title
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    |dw:1324417943491:dw|

    • 2 years ago
  6. davian Group Title
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    so i wud just use the points to find L?

    • 2 years ago
  7. across Group Title
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    That's right; given\[J:(-8,7),\]\[K:(3,4),\]can you find the equation of the line?

    • 2 years ago
  8. across Group Title
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    Remember the point-slope formula\[y=m(x-x_1)+y_1,\]where\[m=\frac{y_2-y_1}{x_2-x_1}.\]

    • 2 years ago
  9. davian Group Title
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    you can yea, but im not sure what formula to use

    • 2 years ago
  10. davian Group Title
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    ohh

    • 2 years ago
  11. across Group Title
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    First find m, and then find the equation. :) Tell me what you get.

    • 2 years ago
  12. davian Group Title
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    i got -3/11 for M

    • 2 years ago
  13. across Group Title
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    That's correct;\[m=-\frac{3}{11}.\]

    • 2 years ago
  14. davian Group Title
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    so thats your cordinates right?

    • 2 years ago
  15. across Group Title
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    That's the slope of the line we're trying to find. To find the equation of the line, we substitute these values into the point-slope equation:\[y=-\frac{3}{11}(x-3)+4.\]Let's simplify!

    • 2 years ago
  16. across Group Title
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    (We're almost done, too!)

    • 2 years ago
  17. davian Group Title
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    i got -0.86 which i think is way off?..

    • 2 years ago
  18. across Group Title
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    For the equation of the line, I got\[y=-\frac{3}{11}x+\frac{53}{11}.\]Do you agree with this?

    • 2 years ago
  19. davian Group Title
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    yea im sure you did it right im just not sure what u did?...(this is why geometry confuses me)

    • 2 years ago
  20. across Group Title
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    I only did one thing: I found the equation of the line formed by the points J and K.

    • 2 years ago
  21. davian Group Title
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    i understand that, im just not sure what steps u used, after we got -3/11 i got lost after that (sorry i dont mean to make things difficult)

    • 2 years ago
  22. across Group Title
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    hey, no probs :) right after we found m=-3/11, i plugged all the values we know into the point-slope equation\[y=m(x-x_1)+y_1.\]we know that \(m=-3/11\), \(x_1=3\) and \(y_1=4\). After plugging those values into the equation, we get\[y=-\frac{3}{11}(x-3)+4.\]Then I simplified that! :)

    • 2 years ago
  23. davian Group Title
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    o i got that equation but when i simplified it i got -0.86 for some reason

    • 2 years ago
  24. across Group Title
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    After distributing, you should get a term having an x in it:|dw:1324419228233:dw|

    • 2 years ago
  25. davian Group Title
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    oh i changed -3/11 to a fraction thats why i got confused i think

    • 2 years ago
  26. davian Group Title
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    i mean a decimal not a fraction

    • 2 years ago
  27. across Group Title
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    you simplify it more, and you get\[y=-\frac{3}{11}x+\frac{53}{11}\] :)

    • 2 years ago
  28. across Group Title
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    The final step is at hand! Are you ready for it?

    • 2 years ago
  29. davian Group Title
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    Yes Ma'am

    • 2 years ago
  30. across Group Title
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    Now, we know that the x-distance from point J to point K is 11, right? J:(-8*,7) K:(3*,4) 8+3=11

    • 2 years ago
  31. across Group Title
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    If we go 11 units to the left of -8, what do we get?

    • 2 years ago
  32. davian Group Title
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    -19?

    • 2 years ago
  33. across Group Title
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    Yes! Finally, plug -19 into the equation we obtained above, and you'll get the y-coordinate of point L! :)

    • 2 years ago
  34. davian Group Title
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    y=m(x−x1)+y1, that formula?

    • 2 years ago
  35. across Group Title
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    This one\[y=-\frac{3}{11}x+\frac{53}{11}.\]:)

    • 2 years ago
  36. davian Group Title
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    i got -4/11 ? is that right?

    • 2 years ago
  37. across Group Title
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    \[-\frac{3}{11}\cdot(-19)+\frac{53}{11}=\frac{57}{11}+\frac{53}{11}=\frac{110}{11}=10\]

    • 2 years ago
  38. davian Group Title
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    ohh i added -57 to 53

    • 2 years ago
  39. across Group Title
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    Yeah, the signs can become a pain at times. ^^

    • 2 years ago
  40. davian Group Title
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    haha yeah thank you for your help

    • 2 years ago
  41. across Group Title
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    Anyway, there's your answer! The coordinates of point L are (-19,10). I know the process may feel a bit lengthy *looks up*, but it's really not when you give it a second look. :)

    • 2 years ago
  42. davian Group Title
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    thank you soo much for walking through it and helping me i really appreciate it

    • 2 years ago
  43. across Group Title
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    you're most welcome!

    • 2 years ago
  44. davian Group Title
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    (:

    • 2 years ago
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