Find the point on the line y = 3x + 4 that is closest to the origin.?

NetherCraft 0

(Give your answers correct to three decimal places.)

3 Answers

  • Take a line that is perpendicular to this line that also passes through the origin.

    y = 3x + 4

    m = 3

    m * n = -1

    3 * n = -1

    n = -1/3

    y = (-1/3) * x + b

    0 = (-1/3) * 0 + b

    0 = b

    y = (-1/3) * x

    (-1/3) * x = 3x + 4

    -10/3 * x = 4

    x = 4 * 3 / (-10)

    x = 12 / (-10)

    x = -6/5

    y = 3x + 4

    y = 3 * (-6/5) + 20/5

    y = -18/5 + 20/5

    y = 2/5

    (-6/5 , 2/5)

  • That’s when y = 0 so x = -4/3 or – 1.333 and x = 0 so y = 4

  • (-1,0)

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