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

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

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.^^