What is the point that divides the directed line segment from point A to point B in a 2:1 ratio? Point A = (6,-1) Point B = (-3,-3)

Answer 1

The great thing about points on the x-y plane is that you can calculate the x's and y's separately and it works fine.

If you want to divide the segment into a 2:1 ratio, you can think of it as dividing the segment into 3 parts and going 2/3s of the way from point A to point B.

To calculate the x of that point, start with x=6 at point A, and add 2/3s of the "displacement" from 6 to -3. Because you are going in a negative direction, the displacement is -9. So the x of the point is 6+2/3(-9)=0.

Similarly, start with y=-1 at point A. The displacement from -1 to -3 is -2. So the y of the point is -1+2/3(-2)= -2 1/3.

So the point is (0,-2 1/3)