Mathematics

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Find the distance from the point (3, 2) to the line y = 3x + 2.

  • Mathematics -

    Well, you can memorize a formula that Reiny knows or you can figure it out.

    First sketch a graph

    find the line perpendicular to the given line that passes through the given point.

    the slope of the given line is 3
    so the slope of our perpendicular line is -1/3
    so
    y = -x/3 + b is our perpendicular line but what is b?
    put in (3,2)
    2 = -3/3 + b
    b = 3
    so
    y = -x/3 + 3
    Now where do these lines cross?
    y = -x/3 + 3
    y = 3 x + 2
    ------------- subtract
    0 = - 10/3 x + 1
    10 x = 3
    x = 3/10
    then
    y = 9/10 + 20/10 = 29/10

    so
    d^2 = (3-3/10)^2 +( 2 - 29/10)^2

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