Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 9) internally in the ratio 2 : 3.
A. \((5\frac{2}{3}, \frac{2}{5})\)
B. \((\frac{2}{5}, 5\frac{2}{5})\)
C. \((\frac{2}{5}, 2\frac{2}{5})\)
D. \((\frac{-2}{5}, 5\frac{2}{5})\)
Correct Answer: B
Explanation
\((x = \frac{nx_{1} + mx_{2}}{n + m}, y = \frac{ny_{1} + my_{2}}{n + m})\)
Given P(-2, 3) and Q(4, 9),
\((\frac{2(4) + 3(-2)}{2 + 3}, \frac{2(9) + 3(3)}{2 + 3})\)
= \((\frac{2}{5}, \frac{27}{5})\)
= \((\frac{2}{5}, 5\frac{2}{5})\)
