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Thread: Analytic Geometry Q3

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

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

    Attempt:

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

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

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

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

    Finding the value of k:

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

    $\displaystyle 4k +13 = 9$

    $\displaystyle 4k = 13 - 9$

    $\displaystyle 4k = -4$

    $\displaystyle k = \frac{-4}{4}$

    $\displaystyle k = -1$

    Is my answer correct?
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  2. #2
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    Hello, looi76!

    Excellent work!

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


    $\displaystyle 4k +13 = 9$

    $\displaystyle 4k = 13 - 9$

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

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

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