Question

Find the coordinates of the points which divide the line segment joining $A(-2,2)$ and $B(2,8)$ into four equal parts.

Answer 1

From the figure, it can be observed that points $X,Y,Z$ are dividing the line segment in a ratio $1:3,1:1,3:1$ respectively.

Using Sectional Formula, we get,
Coordinates of $X=\frac{1\times 2+3\times (-2)}{1+3},\frac{1\times 8+3\times 2}{1+3})$
$=(-1,\frac{7}{2})$
Coordinates of $Y=\frac{2-2}{2},\frac{2+8}{2}=(0,5))$
Coordinates of $Z=(\frac{3\times 2+1\times (-2)}{1+3},\frac{3\times 8+1\times 2}{1+3})$
$=(1,\frac{13}{2})$