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Thread: Analytic Geometry Q1

  1. #1
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    Analytic Geometry Q1

    Question:
    If $\displaystyle (-3,y)$ is equidistant from $\displaystyle (2,6)$ and$\displaystyle (7,-2)$, find $\displaystyle y$.

    Attempt:

    Distance between two points : $\displaystyle \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

    Distance between $\displaystyle (-3,y)$ and $\displaystyle (2,6) $

    $\displaystyle = \sqrt{ (2--3)^2 + (6-y)^2 }$

    $\displaystyle = \sqrt{ 25 + 36 - 12y + y^2}$

    $\displaystyle = \sqrt{ 61 - 12y + y^2}$


    Distance between $\displaystyle (-3,y)$ and $\displaystyle (7,-2)$

    $\displaystyle = \sqrt{ (7--3)^2 + (-2-y)^2 }$

    $\displaystyle = \sqrt{ 100 + 4 + 4y + y^2 }$

    $\displaystyle = \sqrt{ 104 + 4y + y^2 }$

    Finding the value of $\displaystyle y$.

    $\displaystyle \sqrt{ 61 - 12y + y^2} = \sqrt{ 104 + 4y + y^2 }$

    $\displaystyle 61 - 12y + y^2 = 104 + 4y + y^2 $

    $\displaystyle 61 - 12y = 104 + 4y$

    $\displaystyle 61 - 104 = 4y + 12y$

    $\displaystyle -43 = 16y$

    $\displaystyle y = -\frac{43}{16}$

    Is my answer correct?
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