Question

Using the image below, find the x value for the point that divides the line segment AB into a ratio of 2:3.

Answer 1

Where is the picture?

Answer 2

if the ratio is 2:3, then the simplest way to find the fraction of the total length that each new part will take up. x+y=1 and 2x=3y so solving will give you that x=2/5 and y=3/5.

now you just need to take the length of AB, and multiply it by 2/5 and that will be your x position (assuming you start at x=0..)

Answer 3

The easiest way to do is if A=(a,b) and B=(c,d) is to compute
U=3/5A + 2/5 B= ( 3/5 a + 2/5 c, 3/5 b + 2/5 d)
The point U will do it.