Calculus

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

  • Calculus -

    find slope of original line
    y = 3 x + 4
    so slope = m = 3
    so slope of line perpendicular to original = m' = -1/m = -1/3
    so find line through (-5,0) with slope m' of -1/3
    y = -x/3 + b
    0 = 5/3 + b
    b = -5/3
    so y = -x/3 -5/3
    3y= -x - 5 or x + 3y + 5 = 0
    find intersection of lines
    -9x + 3y -12 = 0
    +1x + 3y + 5 = 0
    ------------------
    8 x -17 = 0
    x = 17/8
    find y
    then find the difference in distance between the two points
    d^2 = change in x^2 + change in y^2

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