The coordinates of the point P dividing the line segment joining the points

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).