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Math Help - Analytic Geometry Q3

  1. #1
    Member looi76's Avatar
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    Analytic Geometry Q3

    Question:
    Find the value of k if (0,2) is equidistant from the points (3,k) and (k,5).

    Attempt:

    Distance between points (0,2) and (3,k):

    = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
    = \sqrt{(3-0)^2+(k-2)^2}
    = \sqrt{9+k^2-4k+4}
    = \sqrt{k^2+4k+13}

    Distance between points (0,2) and (k,5):

    = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
    = \sqrt{(k-0)^2+(5-2)^2}
    = \sqrt{k^2+9}

    Finding the value of k:

    \sqrt{k^2+4k+13} = \sqrt{k^2+9}

    4k +13 = 9

    4k = 13 - 9

    4k = -4

    k = \frac{-4}{4}

    k = -1

    Is my answer correct?
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  2. #2
    Super Member

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    Hello, looi76!

    Excellent work!

    Just a silly error near the end . . . the slap-head type . . .


    4k +13 = 9

    4k = 13 - 9

    4k = {\color{red}-}4

    Of course, 13-9 \:=\:{\color{red}+}4

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