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

• A. (2,4)
• B. (3,5)
• C. (4,2)
• D. (5,3)

Answer 1

The correct option is B (3,5)

Let P(x,y) divides line segment joining A(1,3) and B(4,6) in the ratio 2 : 1.
we know that, the coordinates of a point (x,y) dividing the line segment joining the points
$(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m_1:m_2$ are given by
$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$ and $y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$
$\therefore Herex=\frac{2\left(4\right)+1\left(1\right)}{2+1}$ and $y=\frac{2\left(6\right)+1\left(3\right)}{2+1}$
$\Rightarrow x=\frac{9}{3}andy=\frac{15}{3}\Rightarrow x=3andy=5$
Thus, (3,5) divides the line segment AB in the ratio 2 : 1