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Math Help - Geometry Finding a coordinate

  1. #1
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    Geometry Finding a coordinate

    Given A(2,12) and B(5,0) find the coordinates of P such that P seperates AB in two two parts with a ratio 2 to 1? I do not know how to set this problem up please help me. Thank you
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  2. #2
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    Hello, IDontunderstand!

    Given A(2,12) and B(5,0), find the coordinates of point P
    that seperates AB into two parts with ratio 2:1.

    If P is \tfrac{2}{3} of the way from A to B, then:
    . . the x-coordinate is \tfrac{2}{3} of the way from 2 and 5 (the two x-coordinates)
    . . the y-coordinate is \tfrac{2}{3} of the way from 12 and 0 (the two y-coordindates).

    . . . . \begin{array}{ccccc}x &=& 2 + \tfrac{2}{3}(5-2) &=& 4 \\ \\[-4mm] y &=& 12 + \tfrac{2}{3}(0-12) &=& 4 \end{array}


    Therefore: . P(4,4)

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