Question

What are 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.
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 $Z=(\frac{3\times 2+1\times (-2)}{3+1},\frac{3\times 8+1\times 2}{3+1})$
$=(1,\frac{13}{2})$