Calculus

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Find the point on the line 6 x + 4 y - 1 =0 which is closest to the point ( 0, -1 ).

  • Calculus -

    rewrite as
    y = -(6/4)x + 1/4

    line perpendicular has slope +4/6 = +2/3
    y = (2/3) x + b
    we want it through 0, -1
    -1 = (2/3) 0 + b
    b = -1
    so
    y = (2/3) x - 1
    where does that hit original line?
    (2/3) x - 1 = -(3/2) x + 1/4
    4 x - 6 = -9 x + 3/2
    13 x = 15/2
    x = 15/26
    then y = 5/13

    now find the distance from
    (0,-1) to (15/26 , 5/13) yuuk
    check my arithmetic !

  • Calculus -

    the distance is sqrt(x2-x1)^2+(y2 -y1)^2)?


    will that be a form of interval?

  • Calculus -

    it sid the distance formula isn't what they're looking for, they're looking for interval

  • Calculus -

    Oh, well I guess I found your point :)
    (15/26,5/13)

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