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

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.

Coordinate of X = \(( \frac{1×2+3×(-2)}{1+3} , \frac{1×8+3×2}{1+3} ) \)
\( =( \frac{2-6}{4} , \frac{8+6}{4} ) \)
\( = ( \frac{-4}{4} , \frac{14}{4} ) \)
\( = ( -2 , \frac{7}{2} )\)
Coordinate of Y = \(( \frac{1×2+1×(-2)}{1+1} , \frac{1×8+1×2}{1+1} ) \)
\( =( \frac{2-2}{2} , \frac{8+2}{2} ) \)
\( = ( \frac{0}{2} , \frac{10}{2} ) \)
\( = ( 0 , 5) \)
Coordinate of Y = \(( \frac{3×2+1×(-2)}{3+1} , \frac{3×8+1×2}{3+1} ) \)
\( =( \frac{6-2}{4} , \frac{24+2}{4} ) \)
\( = ( \frac{4}{4} , \frac{26}{4} ) \)
\( = ( 1 , \frac{13}{2} ) \)