Question

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 is [CBSE 2012]
(a) (2, 4) (b) (3, 5) (c) (4, 2) (d) (5, 3)

Answer 1

Here, the point P divides the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1. Then
$$\begin{gathered} \mathrm{Coordinates}\mathrm{of}P=\left(\frac{2\times 4+1\times 1}{2+1},\frac{2\times 6+1\times 3}{2+1}\right) \\ =\left(\frac{8+1}{3},\frac{12+3}{3}\right) \\ =\left(\frac{9}{3},\frac{15}{3}\right) \\ =\left(3,5\right) \end{gathered}$$
Hence, the correct answer is option (b).