Pre-Calc

I am seeking help with this problem Please...Thank you!

Find the point on the line y=x+3 in the xy-plane that is closest to the point (3, 2)

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asked by Roy
  1. Let P(x,y) be that point.
    Would you agree, that is P is the closest point, then the line from P to (3,2) would be perpendicular to the given line?
    slope of line = 1
    so slope of perpendicular = - 1
    slope of perp. = (y-2)/(x-3)
    so (y-2)/(x-3) = -1
    y - 2 = -x + 3
    but y = x+3
    x + 3 - 2 = -x + 3
    2x = 4
    x = 2
    then y = 2 + 3 = 5

    the closest point is (2,5)

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    posted by Reiny

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