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Math

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The sides of the triangle at right are formed by the graphs of 3x+ 2y = 1, y = x − 2, and −4x+ 9y = 22. Is the triangle isosceles? How do you know?

  • Math - ,

    A rather lengthy question, let's find the intersection points.
    1st and 2nd line:
    3x+2y=1
    3x+2(x-2) = 1
    5x = 5
    x=1 , then y = 1-2 = -1 ----> point A(1,-1)

    2nd and 3rd:
    4x - 9y = -22
    4x - 9(x-2) = -22
    -5x = -40
    x = 8 , then y = 2-8 = -6 ----> point B(5,-6)

    1st and 3rd:
    #1 times 4 --> 12 + 8y = 4
    #3 times 3 --> -12x + 27y = 66
    add them
    35y = 70
    y = 2, then
    3x + 4 = 1
    x = -1 --------> point C(-1,2)

    AB = √((5-1)^2 + (-6+1)^2) = √41
    AC = √(-1-1)^2 + (2+1)^2) = √13
    BC = √((5+1)^2 + (2+6)^2) = √100 = 10

    so what is your verdict?

    (check my arithmetic)

  • Math - ,

    Well, you copied 5 and 8 wrong from the 2nd and 3rd problem to the final calculation.

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