Question

Find the ratio in which $P(4,m)$ divides the line segment joining the points $A(2,3)$ and $B(6,-3)$. Hence find $m$.

• A. $1:1,m=0$
• B. $1:2,m=0$
• C. $1:3,m=1$
• D. None

Answer 1

The correct option is A $1:1,m=0$

Let the ratio be $\lambda :1$

$A(2,3)$ $B(6,-3)$

$4=\frac{(\lambda \times 6)+(1\times 2)}{\lambda +1}$

$4\lambda +4=6\lambda +22\lambda =2\lambda =1Ratio=1:1m=\frac{-3\lambda +3}{\lambda +1}=\frac{-3+3}{2}=0\therefore m=0$