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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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Let A and B be required points such that $PA = AB = BQ$
A divides PQ in the ratio $1:2$ (1/2 Mark)
Coordinates of A are $(\frac{1\times 4+2\times (-1)}{1+2}, \frac{1\times (-3)+2\times 7}{1+2}) = (\frac{2}{3}, \frac{11}{3})$ (1 Mark)
B divides PQ in the ratio $2:1$ (1/2 Mark)
Coordinates of B are $(\frac{2\times 4+1\times (-1)}{2+1}, \frac{2\times (-3)+1\times 7}{2+1}) = (\frac{7}{3}, \frac{1}{3})$ (1 Mark)
A divides PQ in the ratio $1:2$ (1/2 Mark)
Coordinates of A are $(\frac{1\times 4+2\times (-1)}{1+2}, \frac{1\times (-3)+2\times 7}{1+2}) = (\frac{2}{3}, \frac{11}{3})$ (1 Mark)
B divides PQ in the ratio $2:1$ (1/2 Mark)
Coordinates of B are $(\frac{2\times 4+1\times (-1)}{2+1}, \frac{2\times (-3)+1\times 7}{2+1}) = (\frac{7}{3}, \frac{1}{3})$ (1 Mark)