terminal ponits?

Question

The segment joining (1,-3) and (4,-6)is extended a distance equal in one-sixth of its own length. Finf the terminal points.

Answer 1

Its current length is sqrt((4-1)^2+(-6-(-3))^2 = sqrt(18)=3sqrt(2)
1/6 of this length is sqrt(2)/2. The slope of the line is -1.
So the x and y components of this extension x = +/-1/2 And y = +/- 1/2
So just adjust the coordinates by adding +1/2 to (1,-3) if you are extending to the left, or add -1/2 to both (4,-6) if you are extending to the right or ad +/- 1/2 to the two original points if you are extending the line an equal amount in both directions.