Question
Points P, Q, R and S divide the line segments joining the points A(1, 2) and B(6, 7) in five equal parts. Find the coordinates of the points P, Q and R.
✓
Answer
Point P divides line segment AB in the ratio 1 : 4
$\therefore\text{Coordinates of P}=\Big(\frac{1\times6+4\times1}{1+4},\frac{1\times7+4\times2}{1+4}\Big)$
$=\Big(\frac{6+4}{5},\frac{7+8}{5}\Big)$
$=\Big(\frac{10}{5},\frac{15}{5}\Big)$
$=(2,3)$
Point Q divides line segment AB in the ratio 2 : 3,
$\therefore\text{Coordinates of Q}=\Big(\frac{2\times6+3\times1}{2+3},\frac{2\times7+3\times2}{2+3}\Big)$
$=\Big(\frac{12+3}{5},\frac{14+6}{5}\Big)$
$=\Big(\frac{15}{5},\frac{20}{5}\Big)$
$=(3,4)$
Point R divides line segment AB in the ratio 3 : 2,
$\therefore\text{Coordinates of R}=\Big(\frac{3\times6+2\times1}{3+2},\frac{3\times7+2\times2}{3+2}\Big)$
$=\Big(\frac{18+2}{5},\frac{21+4}{5}\Big)$
$=\Big(\frac{20}{5},\frac{25}{5}\Big)$
$=(4,5)$
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