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by Jubi129 on May 5th, 2009

Jubi129

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Find the point on the line -6 x + 5 y + 2 =0 which is closest to the point ( 4, -3 ).

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  • by iwnit on May 7th, 2009

    iwnit

    1) This should help:

    "In algebra, for any linear equation y=mx + b, the perpendiculars will all have a slope of (-1/m), the opposite reciprocal of the original slope. It is helpful to memorize the slogan "to find the slope of the perpendicular line, flip the fraction and change the sign." Recall that any whole number a is itself over one, and can be written as (a/1)
    To find the perpendicular of a given line which also passes through a particular point (x, y), solve the equation y = (-1/m)x + b, substituting in the known values of m, x, and y to solve for b."
    Source and further information:
    http://en.wikipedia.org/wiki/Perpendicular


    2) Put the linear equation in the requested form:
    -6 x + 5 y + 2 =0
    in the form y = m x + b
    y = (6/5)x + (-2/5)
    m = 6/5
    b = -2/5


    3) solve for the equation y = (-1/m)x + b
    with the known values:
    m = 6/5
    x = 4
    y = -3

    The equation can be written:
    -3 = [-1/(6/5)]* 4 + b
    b = [(4*(5/6)]-3 = (10/3)-3 = - 20/3


    4) The perpendicular line has also the equation:
    y = (-1/m)x + b = -(5/6)* x - 20/3
    y = -(5/6)* x - 20/3

    We just need to solve the system of two equations:
    y = -(5/6)* x - 20/3
    -6 x + 5 y + 2 =0

    I leave this part for you...

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