The ratio in which the point $(-4,6)$ divides the line segment joining the points $A(-6,10)$ and $B(

Question

The ratio in which the point $(-4,6)$ divides the line segment joining the points $A(-6,10)$ and $B(3,-8)$ is\

Professor PC Thomas Classes · Answer

(c) : Let point $P(-4,6)$ divides the line segment $A B$ in the ratio $m_{1}: m_{2}$.\ By section formula, we have $$ (-4,6)=\left(\frac{3 m_{1}-6 m_{2}}{m_{1}+m_{2}}, \frac{-8 m_{1}+10 m_{2}}{m_{1}+m_{2}}ight) $$ Now, $-4=\frac{3 m_{1}-6 m_{2}}{m_{1}+m_{2}}$\ $\Rightarrow 3 m_{1}-6 m_{2}=-4 m_{1}-4 m_{2}$\ $\Rightarrow \quad 7 m_{1}=2 m_{2} 	herefore m_{1}: m_{2}=2: 7$\ Putting the value of $m_{1}: m_{2}$ in $y$-coordinate, we get $$ \frac{-8 \frac{m_{1}}{m_{2}}+10}{\frac{m_{1}}{m_{2}}+1}=\frac{-8 	imes \frac{2}{7}+10}{\frac{2}{7}+1}=6 $$ Hence, required ratio is $2: 7$.\