Question

In what ratio does X-axis divide the line segment joining the points $P(4,8)$ and $Q(5,-9)$?

• A. $8:9$
• B. $5:7$
• C. $3:8$
• D. $2:9$

Answer 1

The correct option is A $8:9$

Let the required ratio be $k:1$.

Co-ordinates of points of division are given by Section Formula,

$\Rightarrow \frac{m_1{x}_2+m_2{x}_2}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$ Here, $m_1=k$ and $m_2=1$

If point lies on x-axis, then it will be in the form $(x,0)$

$x=\frac{k\left(8\right)+1\left(4\right)}{k+1}$ and $0=\frac{k(-9)+1\left(8\right)}{k+1}$

$-9k+8=0,k=\frac{-8}{-9},k=\frac{8}{9}$

$\therefore$ Required ratio $k:1$ is $\frac{8}{9}:1$ or $8:9$.