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anonymous

  • one year ago

A triangle has vertices at (2, 4), (-3, -6), and (4, -2). Find its perimeter rounded to two decimal places.

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  1. freckles
    • one year ago
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    I would plot the points so it is easier for me to see which three distances to calculate.

  2. anonymous
    • one year ago
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  3. freckles
    • one year ago
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    |dw:1437665201466:dw|

  4. freckles
    • one year ago
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    |dw:1437665261302:dw| we need to find all three side measurements to do that we can use the distance formula so for example let's go ahead and find the distance between (2,4) and (4,-2) you do that by doing: \[d_1=\sqrt{(2-4)^2+(4-(-2))^2} \\ d_1=\sqrt{(-2)^2+(6)^2} \\ d_1=\sqrt{4+36} \\ d_1=\sqrt{40}\] so we have that|dw:1437665356288:dw| we also need to find the other side lengths you try the other two legs and remember: \[\text{ The distance \between } (x_1,y_1) \text{ and } (x_2,y_2) \text{ is } \\ \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]

  5. freckles
    • one year ago
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    once you find all the side lengths you add the side lengths to find the perimeter

  6. anonymous
    • one year ago
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    ok

  7. freckles
    • one year ago
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    so have you computed the distance between (2,4) and (-3,-6) ?

  8. anonymous
    • one year ago
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    no

  9. freckles
    • one year ago
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    |dw:1437665675706:dw| well you still need to find these two distances (these two side lengths)

  10. anonymous
    • one year ago
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    I got 10

  11. freckles
    • one year ago
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    that is you need to find the distance between (2,4) and (-3,-6) you also need to find the distance between (-3,-6) and (4,-2)

  12. freckles
    • one year ago
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    the distance between (2,4) and (-3,-6) is given by: \[d_3=\sqrt{(2-(-3))^2+(4-(-6))^2}=\sqrt{5^2+(10)^2}\] see if you can finish simplifying this

  13. anonymous
    • one year ago
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    39 and 125

  14. freckles
    • one year ago
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    do you mean sqrt(125) for d_3 ?

  15. anonymous
    • one year ago
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    yes

  16. freckles
    • one year ago
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    |dw:1437665932861:dw| now you just need to find d_2

  17. freckles
    • one year ago
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    which is the distance between (4,-2) and (-3,-6)

  18. freckles
    • one year ago
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    use that formula above to find it

  19. freckles
    • one year ago
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    \[\text{ The distance between } (x_1,y_1) \text{ and } (x_2,y_2) \text{ is } \\ \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \]

  20. anonymous
    • one year ago
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    I got 10

  21. freckles
    • one year ago
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    hmm... that is what you got for the other one... try again... you have (4,-2) and (-3,-6) replace x1 with 4 replace x2 with -3 replace y1 with -2 replace y2 with -6 ... \[d_2=\sqrt{(4-(-3))^2+(-2-(-6))^2}\]

  22. anonymous
    • one year ago
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    11

  23. freckles
    • one year ago
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    4-(-3) is the same as 4+3 -2-(-6) is the same as -2+6

  24. freckles
    • one year ago
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    \[d_2=\sqrt{(4+3)^2+(-2+6)^2}\]

  25. freckles
    • one year ago
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    compute 4+3 and -2+6 then square both results

  26. freckles
    • one year ago
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    then add those results

  27. anonymous
    • one year ago
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    i got 11

  28. freckles
    • one year ago
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    sounds like you are doing (4+3)+(-2+6) which means you are ignoring the squares

  29. freckles
    • one year ago
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    (4+3)^2=(7)^2 (-2+6)^2=(4)^2

  30. freckles
    • one year ago
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    \[d_2=\sqrt{(4+3)^2+(-2+6)^2} \\ d_2=\sqrt{(7)^2+(4)^2}\]

  31. freckles
    • one year ago
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    you square the numbers before adding them because that is what order of operations tells us to do

  32. anonymous
    • one year ago
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    29 65

  33. freckles
    • one year ago
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    don't know where the 29 comes from but sqrt(49+16) is sqrt(65)

  34. anonymous
    • one year ago
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    okay

  35. freckles
    • one year ago
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    |dw:1437666447857:dw| now add all the sides to find the perimeter

  36. anonymous
    • one year ago
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    239

  37. anonymous
    • one year ago
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    230

  38. freckles
    • one year ago
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    so you added sqrt(125) and sqrt(40) and sqrt(65)?

  39. freckles
    • one year ago
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    or did you add 125 and 40 and 65?

  40. freckles
    • one year ago
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    because those aren't the same numbers

  41. anonymous
    • one year ago
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    i added them all

  42. freckles
    • one year ago
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    sqrt(125) is not the same as 125 sqrt(40) is not the same as 40 sqrt(65) is not the same as 65 so adding sqrt(125) and sqrt(40) and sqrt(65) is not equivalent to adding 125 and 40 and 65.

  43. freckles
    • one year ago
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    \[\sqrt{125}+\sqrt{40}+\sqrt{65}\] just enter this into the calculator to get the approximated perimeter

  44. anonymous
    • one year ago
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    25.567

  45. freckles
    • one year ago
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    ok and you are suppose to round to 2 decimal places so that would actually be...

  46. anonymous
    • one year ago
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    25.57

  47. freckles
    • one year ago
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    yes

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