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Math Help - Analytic Geometry Q1

  1. #1
    Member looi76's Avatar
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    Analytic Geometry Q1

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

    Attempt:

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

    Distance between (-3,y) and (2,6)

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

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

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


    Distance between (-3,y) and (7,-2)

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

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

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

    Finding the value of  y.

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

    61 - 12y + y^2 =   104 + 4y + y^2

    61 - 12y  =   104 + 4y

    61 - 104 = 4y + 12y

    -43 = 16y

    y = -\frac{43}{16}

    Is my answer correct?
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  2. #2
    Moo
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