Question

1) Segment CD has endpoints (-4, 3) and (8, -1). Find the coordinates of the point that divides the line segment directed from C to D in the ratio of 2:3.
A) (6/5,26/5)
B) (4/5,7/5)
C) (1/5,13/5)
D) (16/5,3/5)

I would provide what I think the answer is- but I'm really stuck and I don't have any idea. The answer is fine, since that's what I need, but I would love some step to step help.

Answer 1

dividing the line into pieces of the ratio 2:3 means that the desired point is 2/5 of the way from C to D, right?

The directed x-distance from C to D is 12
The directed y-distance from C to D is -4
So for the x-value add 2/5 of 12 to C
Same for the y. add 3/5 of -4 to C

Answer 2

I find that most students find the following method very easy to understand for these type of problems:
Let the point be P(x,y)
For the x,
(x+4)/(8-x) = 2/3
3x + 12 = 16 -2x
5x = 4
x = 4/5 <----- I see that as a choice

Now repeat the same steps for y