Point on a direct line segment?

Question

Let MN be the directed line segment beginning at point M(2,1) and ending at point N(11,-3). Find the point P on the line segment that partitions the line segment into the segments MP and PN at a ratio of 2:3.

Answer 1

If P partitions MN into MP and PN at a ratio of 2:3 then P is 2/5 of the way from M to N in both the X and Y directions.  

 

So the X-coordinate of P is (2/5)*(11-2) + 2 = 18/5 + 10/5 = 28/5 = 5.6 

and the Y-coordinate of P is (2/5)*(-3-1) + 1 = -8/5 + 5/5 = -3/5 = -0.6 

 

So P = (5.6,-0.6)