How do I find the middle(1/2), 1/3, 1/4, etc, of a line? Similar to this question: How to calculate the middle of a line? where it's explained how to find the middle of a line (x,y), so that's half the line 1/2, but I also need to find one third of the line, one fourth, and so on.
I tried dividing by 4 instead of 2 to get 1/4 but it didn't seem to work:
1/2 (works):
$x = \dfrac{x_1 + x_2}{2}$ $y = \dfrac{y_1 + y_2}{2}$
1/4 (doesn't work):
$x = \dfrac{x_1 + x_2}{4}$ $y = \dfrac{y_1 + y_2}{4}$

Divide your segment into even parts. 

From the last point you can find that
$$
x_2 = x_1 + n\Delta \implies \Delta = \frac {x_2 - x_1}n
$$
You need to find second point in that division, so
$$
x' = x_1 + \Delta = x_1 + \frac {x_2-x_1}n = \frac {n-1}n x_1 + \frac 1n x_2
$$
So, let's say you want to divide your segment into 2 even parts, then $n = 2$ and 
$$
x' = \frac {x_1}2 + \frac {x_2}2
$$
If $n = 3$ (3 even parts)
$$
x' = \frac 23 x_1 + \frac 13 x_2
$$
$n = 4$ (4 even parts)
$$
x' = \frac 34 x_1 + \frac 14 x_2
$$
