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anonymous

  • one year ago

Determine if triangle DEF with coordinates D (3, 2), E (4, 6), and F (7, 3) is an equilateral triangle. Use evidence to support your claim. If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific.

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  1. anonymous
    • one year ago
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    I used the distance formula for each segment in triangle DEF and have come to the conclusion that the triangle is not an equilateral triangle. The distance for Segments DE and DF are sq.rt.17, but the distance for Segment EF is sq.rt. 18. I am having difficulty answering the second part of the question, "If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific." Please provide guidance as to how to go about answering this question. Thank you!

  2. anonymous
    • one year ago
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    Find the distance between D and E to determine the length of Segment DE. D = (3,2) and E = (4,6) Step 1: d = sq.rt. (x2 - x1)^2 + (y2 - y1)^2 Step 2: d = sq.rt. (4 - 3)^2 + (6 - 2)^2 Step 3: d = sq.rt. (1)^2 + (4)^2 Step 4: d = sq.rt. 1 + 16 Step 5: d = sq.rt. 17 Find the distance between E and F to determine the length of Segment EF. E = (4,6) and F = (7,3) Step 1: d = sq.rt. (x2 - x1)^2 + (y2 - y1)^2 Step 2: d = sq.rt. (7 - 4)^2 + (3 - 6)^2 Step 3: d = sq.rt. (3)^2 + (-3)^2 Step 4: d = sq.rt. 9 + 9 Step 5: d = sq.rt. 18 Find the distance between D and F to determine the length of Segment DF. Step 1: d = sq.rt. (x2 - x1)^2 + (y2 - y1)^2 Step 2: d = sq.rt. (7 - 3)^2 + (3 - 2)^2 Step 3: d = sq.rt. (4)^2 + (1)^2 Step 4: d = sq.rt 16 + 1 Step 5: d = sq.rt. 17

  3. DanJS
    • one year ago
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    i guess, sqrt(18) - sqrt(17) needs to be taken off EF, and recalculate the position of one of the points

  4. anonymous
    • one year ago
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    I agree, but I have tried different combinations and have failed to find an alternative point.

  5. Loser66
    • one year ago
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    By distance formula , you have \(EF =\sqrt{(7-4)^2+(3-6)^2}=\sqrt {18}\) Only one way you can do is to make it down to \(\sqrt{17}\)

  6. anonymous
    • one year ago
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    That is what I thought before, but I got points off because I didn't give an alternative point.

  7. Loser66
    • one year ago
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    by changing the location of E. F cannot be changed because it relates to D

  8. Loser66
    • one year ago
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    if E( 6, 7) then you get the required triangle.

  9. anonymous
    • one year ago
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    Seriously!?!

  10. Loser66
    • one year ago
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    Read the problem, they say : by what changes??

  11. anonymous
    • one year ago
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    Yes, thank you so much!

  12. Loser66
    • one year ago
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    my change is the point E from (4, 6) to (6,7)

  13. DanJS
    • one year ago
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    E or F can move in a circle around point D, right

  14. Loser66
    • one year ago
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    @DanJS It is a good idea but I don't think they use the orbit concept here.

  15. anonymous
    • one year ago
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    I plugged in 6,7 yet still got different measures for each distance. Did I do something wrong?

  16. Loser66
    • one year ago
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    oh, yea!! I am wrong!!

  17. Loser66
    • one year ago
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    since if you change E, then DE changes also. OMG. I am terribly sorry.

  18. anonymous
    • one year ago
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    No worries!!

  19. DanJS
    • one year ago
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    I dont see how that has to happen, if you move E , DE can stay the same length, the radius of the circle, when you move E on an Arc towards F

  20. DanJS
    • one year ago
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    or F towards E the same way

  21. anonymous
    • one year ago
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    Circle?

  22. Loser66
    • one year ago
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    I know how to do!! Thanks God. He gives me a chance to fix my mistake. hehehe.

  23. anonymous
    • one year ago
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    Lol thank you both for your help and patience!

  24. DanJS
    • one year ago
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    Circle centered at D, radius root(17), you just swing F towards E or E towards F, till the chord EF is root17

  25. DanJS
    • one year ago
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    i am guessing

  26. DanJS
    • one year ago
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    or set up two distance formula , and use (x,y) for F, and figure out x and y, possibly

  27. Loser66
    • one year ago
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    OK. \(DF=\sqrt{17}\)

  28. anonymous
    • one year ago
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    I tried your second option, but every time I changed a coordinate, I failed to get the same measure for each segment.

  29. Loser66
    • one year ago
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    \(DE=\sqrt{(x_E-3)^2+(y_E-2)^2)}\) \(EF=\sqrt{(7-x_E)^2+(3-y_E)^2)}\)

  30. Loser66
    • one year ago
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    and we want DE = EF, so, solve for it!!

  31. Loser66
    • one year ago
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    \(DE = EF = \sqrt{17}\)

  32. DanJS
    • one year ago
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    that what i said.. :)

  33. Loser66
    • one year ago
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    ok, take over, please. hehehe.. I tried to fix my mistake but if you know how to do, please, finish the stuff. I am not good at explaining. Please :)

  34. anonymous
    • one year ago
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    So the change or different coordinate is (x,y)?

  35. DanJS
    • one year ago
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    there are two possible points for F, one on each side of the Y axis, i think

  36. DanJS
    • one year ago
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    17 = (x-4)^2 + (y-6)^2 17 = (x-3)^2 + (y-2)^2 i solved those with a computer,

  37. anonymous
    • one year ago
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    So D still equals (3,2)...E still equals (4,6). What does F = ?

  38. DanJS
    • one year ago
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    \[F(x,y) = (\frac{ 4\sqrt{3} + 7 }{ 2 } , \frac{ 8-\sqrt{3} }{ 2 }) \approx (6.9641, 3.1340)\]

  39. anonymous
    • one year ago
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    Woah...that is very precise. I think I may have gone about answering this question the wrong way because I doubt my teacher would have expected such an answer.

  40. anonymous
    • one year ago
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    Do you think I should answer using your original suggestion, "i guess, sqrt(18) - sqrt(17) needs to be taken off EF, and recalculate the position of one of the points,"....?

  41. DanJS
    • one year ago
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    \[FD = FE = \sqrt{17}\] that what those 2 distance equations above are

  42. anonymous
    • one year ago
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    Thank you for your help and time! If you could, would you please help me formulate my final answer. If not, I totally understand because I have already taken up so much of your time!!

  43. DanJS
    • one year ago
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    draw a picture first

  44. DanJS
    • one year ago
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    label everything

  45. DanJS
    • one year ago
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    then maybe, move F up a little, and relable that F' point (x,y), EF' = root (17) to make an equilateral triangle

  46. DanJS
    • one year ago
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    then use the work above

  47. anonymous
    • one year ago
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    Okay, that is perfect! Thanks again. Can I give you multiple awards...other than just a medal?

  48. anonymous
    • one year ago
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    *other not multiple

  49. DanJS
    • one year ago
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    only things i know are fan and testimonial

  50. anonymous
    • one year ago
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    Testimonial?

  51. DanJS
    • one year ago
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    @Loser66 did just as much...

  52. DanJS
    • one year ago
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    hover over name, and buttons are there

  53. anonymous
    • one year ago
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    Okay, I gave you a medal, became a fan and submitted a testimonial. Thanks!!

  54. DanJS
    • one year ago
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    hah, thanks, ill fan you to

  55. anonymous
    • one year ago
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    No need!! Good night!!

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