Question

In what ratio does the point $P(2,\frac{-5}{6})$ divide the line segment joining the points A(-3,5) and B(3,-2)?

• A. $1:5$
• B. $5:1$
• C. $2:3$
• D. $3:5$

Answer 1

The correct option is B $5:1$

Let the required ratio be $m_1,m_2$

Let $(x_1,y_1)=(-3,5)$

$(x_2,y_2)=(3,-2)$

and $(x,y)=(2,\frac{-5}{6})$

By Section Formula,

$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$

$\Rightarrow 2=\frac{m_1\times 3+m_2\times -3}{m_1+m_2}$

$\Rightarrow 2m_1+2m_2=3m_1-3m_2$

$\Rightarrow 2m_1-3m_1=-3m_2-2m_2$

$\Rightarrow -m_1=-5m_2$

$\Rightarrow \frac{m_1}{m_2}=\frac{5}{1}$

$\therefore$Required Ratio=5:1