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