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.