analytic geometry

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The segment joining (-1,4), (2,-2) is extended three times its own length. Find the terminal points.

  • analytic geometry -

    let the end point be (x,y)

    for the x-coordinate:
    (x+1)/(2+1) = 3/1
    x+1 =9
    x = 8

    for the y-coordinate:
    (y-4)/(-2-4) = 3/1
    y-4 = -18
    y = -14
    one end point is (8,-14)

    we could have extended it the other way ...
    (x-2)(-1-2) = 3/1
    x-2 = -9
    x= -7

    (y+2)/(4+2) = 3/1
    y+2 = 18
    y = 16
    in that direction the point is (-7,16)

    check my arithmetic.

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