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Math Help - division of line segments (midpoints)

  1. #1
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    division of line segments (midpoints)

    a segment joining (-2, -3), (6, 1) is extended each way a distance equal to one-fourth of its own length. find the terminal points.

    for the (+, +) i got the answer (10, 2) but according to the book, the answer is (8, 2) and (-4, -4) on the (-, -). i haven't tried solving for the later.

    please help. im so tired thinking where i messed up
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  2. #2
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    Hello, proview!

    Did you make a sketch?
    You can "eyeball" the problem . . .


    A segment joining (-2, -3), (6, 1) is extended each way a distance
    equal to one-fourth of its own length. .Find the terminal points.
    Code:
                                              C(8,2)
                                      B       o
                                    (6,1) *   :1
                                      o - - - *
                                  *   :   2
                              *       :
                        - *           4
                      *               :
                  *                   :
            A o - - - - - 8 - - - - - *
           (-2,-3)

    Going from A to B, we move 8 units right, 4 units up.
    To extend AB by \tfrac{1}{4} its length,
    . . move 2 units right \left(\tfrac{1}{4}\text{ of 8}\right), and 1 unit up \left(\tfrac{1}{4}\text{ of 4}\right)
    And we arrive at C(8,2)

    Repeat the process at the other end.

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  3. #3
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    Nov 2008
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    yeah i can see that. but what formula can i use? the formula for midpoints that we are using are:

    midpoint(x) = 1/2 (X1 + X2)
    midpoint(y) = 1/2 (Y1 + Y2)

    how can i derive one that will get me 1/4 of its length or 1/8? 1/5... and so on..

    thanks in advance.^^
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