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.
((5frac{2}{3}, frac{2}{5})) -
B.
((frac{2}{5}, 5frac{2}{5})) -
C.
((frac{2}{5}, 2frac{2}{5})) -
D.
((frac{-2}{5}, 5frac{2}{5}))
Correct Answer: Option 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}, 5frac{2}{5}))