# Math Help - division of line segments (midpoints)

1. ## 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.

2. 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.

3. 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..