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Math Help - Graphing

  1. #1
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    Post Graphing

    Determine a value for k so that the point (1,k) is the same distance from the line x= -2 as it is from the point (2,0).
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  2. #2
    MHF Contributor
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    Quote Originally Posted by katchat64 View Post
    Determine a value for k so that the point (1,k) is the same distance from the line x= -2 as it is from the point (2,0).
    Here is one way of doing this.

    The point (1,k) is anywhere on the vertical line x=1.
    The distance of vertical line (x=1) from the vertical line (x = -2) is 3 units.
    The distance of (1,k) from (2,0) can be found by the distance formula.
    So,
    3 = sqrt[(1-2)^2 +((k-0)^2]
    3 = sqrt[1 +k^2]
    Square both sides.
    9 = 1 +k^2
    k^2 = 9 -1 = 8
    k = +,-sqrt(8) = +,-2sqrt(2) --------answer.

    -------------
    Check if (1, +,-2sqrt(2)) is 3 units away from (2,0):
    d = sqrt[(1 -2)^2 +(+,-2sqrt(2) -0)^2]
    d = sqrt[(1) +4(2)]
    d = sqrt(9) = 3 ------it is, so, okay.
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