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 is B

\((x = \frac{nx_{1} + mx_{2}}{n + m}, y = \frac{ny_{1} + my_{2}}{n + m})\)

Given P(-2, 3) and Q(4, 9),

\((\frac{2(4) + 3(-2)}{2 + 3}, \frac{2(9) + 3(3)}{2 + 3})\)

= \((\frac{2}{5}, \frac{27}{5})\)

= \((\frac{2}{5}, 5\frac{2}{5})\)