Thread: division of line segments (midpoints)

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 to , we move 8 units right, 4 units up.
To extend by its length,
. . move 2 units right , and 1 unit up
And we arrive at

Repeat the process at the other end.

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.^^