Find the point Q along the directed line segment from point R(-3,3) to point S(6,-3) that divides the segment to the ratio 2:1

Question

A. (0,1)

B. (6,-4)

C. (3,-1)

D. (3,0)

Answer 1

The length of the line segment is (6, -3) - (-3, 3) = (9, -6).

That's 9 units in the X-direction and -6 in Y.

The X and Y dimensions will be split in the 2:1 ratio.

X, starting at -3, will move 2/3 of the 9 = 6

The new X will be -3+6 = 3.

Starting at 3, Y will move 2/3 of -6 = -2

The new Y will be 3-2 = 1.

Q = (6, -1)

This does not match any of the answer choices. Either you or the problem author has swapped something. Maybe it's just a sign error! Be careful. The from/to is important and it has to match the ratio direction. You can see what is involved in the solution from my description. The X and Y components of the line segment will each be split in the 2:1 ratio. A simple diagram can help you visualize this type of problem if things just refuse to make sense!