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 is observed that points P,Q,R are dividing the line segment in a ratio 1:3,1:1,3:1 respectively,
Coordinates of P=$(\frac{1\times2+3\times(-2)}{1+3},\frac{1\times8+3\times2}{1+3})$=$(-1,\frac{7}{2})$
Coordinates of Q= $(\frac{2+(-2)}{2},\frac{2+8}{3+1})=(0,5)$
Coordinates of R= $(\frac{3\times2+1\times(-2)}{1+3},\frac{3\times8+1\times2}{3+1})=(1,\frac{13}{2})$