148
Find the coordinates of the points which divide the line segment joining points P($-1, 7$) and Q($4, -3$) into three equal parts.
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OR
(b)
Let A and B be required points such that PA = AB = BQ
A divides PQ in the ratio $1 :2$
Coordinates of A are $(\frac{1\times 4+2\times(-1)}{1+2}, \frac{1\times(-3)+2\times 7}{1+2})$ (1/2 Mark)
$= (\frac{2}{3}, \frac{11}{3})$ (1 Mark)
B divides PQ in the ratio $2 : 1$
Coordinates of B are $(\frac{2\times 4+1\times(-1)}{2+1}, \frac{2\times(-3)+1\times 7}{2+1})$ (1/2 Mark)
$= (\frac{7}{3}, \frac{1}{3})$ (1 Mark)
(b)
Let A and B be required points such that PA = AB = BQ
A divides PQ in the ratio $1 :2$
Coordinates of A are $(\frac{1\times 4+2\times(-1)}{1+2}, \frac{1\times(-3)+2\times 7}{1+2})$ (1/2 Mark)
$= (\frac{2}{3}, \frac{11}{3})$ (1 Mark)
B divides PQ in the ratio $2 : 1$
Coordinates of B are $(\frac{2\times 4+1\times(-1)}{2+1}, \frac{2\times(-3)+1\times 7}{2+1})$ (1/2 Mark)
$= (\frac{7}{3}, \frac{1}{3})$ (1 Mark)