Math-Calculus

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Find the point on the line -2x + 4y + 3 =0 which is closest to the point (-2,1). Note: I have been struggling on this for hours!

  • Math-Calculus -

    For hours ???

    Slope of the given line is 1/2
    so the slope of the line through (-2,1) and perpendicular to it must be -2
    equation of that perp.
    y = -2x + b, with (-2,1) lying on it, thus ...
    1 = -2(-2) + b
    -3 = b

    y = -2x - 3
    solve the two equations to get the required point
    -2x + 4y + 3 = 0
    -2x + 4(-2x-3) + 3 = 0
    -2x -8x - 12 + 3 = 0
    -10x = 9
    x = -9/10
    sub that back into y = -2x-3
    y = -2(-9/10) - 3 = -6/5

    the point is (-9/10 , -6/5)

  • Math-Calculus -

    Thank you very much Reiny for this wonderful explanation. I am not the brightest bulb and yes 2 hours to be precise.

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