We are given points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex].
We first find the midpoint M, of AB, which divides the segment AB into 2 equal parts,
then we find the midpoint N of AM, and midpoint K of MB.
Thus each of the half parts is divided into 2 equal parts. The whole segment is divided into 4 equal parts.
The coordinates of M, N and K are found as follows:
the coordinates of M are: [tex]( \frac{x_1+x_2}{2} , \frac{y_1+y_2}{2}) [/tex]
the coordinates of N are:
[tex]\displaystyle{( \frac{x_1+\frac{x_1+x_2}{2}}{2} , \frac{y_1+\frac{y_1+y_2}{2}}{2})=( \frac{\frac{2x_1+x_1+x_2}{2}}{2} , \frac{\frac{2y_1+y_1+y_2}{2}}{2}) [/tex]
[tex]=\displaystyle{(\frac{3x_1+x_2}{4}, \frac{3y_1+y_2}{4})}[/tex]
similarly, the coordinates of k are:
[tex]=\displaystyle{(\frac{x_1+3x_2}{4}, \frac{y_1+3y_2}{4})}[/tex]
