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

asked by sze
  1. Take any point on the line as (x,y)

    Now, distance between the point on the line and the given point = d

    => d^2 = (x-4)^2 + (y-5)^2

    You can treat this as a function. When d^2 is minimum, then d will be minimum too.

    function to minimize = (x-4)^2 + (y-5)^2

    But, y can be written in terms of x:
    3x + 2y = 5
    => y = (5-3x)/2

    So, by minimizing the function
    f(x) = (x-4)^2 + ((-3x-5)/2)^2
    You will get the required point.

    posted by Arora

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