If  P  and Q are the points with coordinates  (-3, 4) and (2, 1) respectively, then the coordinates of the point  R on  PQ produced such that PR = 2QR  are:

Solution:
Let $$P = (x_1, y_1) = (-3, 4), \quad Q = (x_2, y_2) = (2, 1) \\$$​​
Given: PR = 2QR $$\Rightarrow$$​ R divides PQ externally in the ratio 1 : 2
Using external division formula:
​$$x = \frac{m x_1 - n x_2}{m - n}, \quad y = \frac{m y_1 - n y_2}{m - n} \\$$​​
Here m = 1,  n = 2
So,
​$$\begin{aligned}x &= \frac{1(-3) - 2(2)}{1 - 2} = \frac{-3 - 4}{-1} = \frac{-7}{-1} = 7 \\y &= \frac{1(4) - 2(1)}{1 - 2} = \frac{4 - 2}{-1} = \frac{2}{-1} = -2\end{aligned}$$​​
Coordinates of point  R are (7, -2)
Correct answer is (b)