Question

If the point $(2,a)$ divides the line segment joining the points $(-4,3)$ and $(6,3),$ then

• A. the ratio is $2:3$
• B. the ratio is $3:2$
• C. the value of $a$ is $3$
• D. the value of $a$ is $2$

Answer 1

Answer: (B), (C)

The correct options are
B the ratio is $3:2$
C the value of $a$ is $3$

Let the given point $C(2,a)$ divides the line segment joining the points $A(-4,3)$ and $B(6,3)$ in the ratio $k:1$.
Then, $(\frac{6k-4\left(1\right)}{k+1},\frac{3k+3\left(1\right)}{k+1})=(2,a)$
$\Rightarrow \frac{6k-4}{k+1}=2\Rightarrow k=\frac{3}{2}$ ​

$\frac{3k+3}{k+1}=a\Rightarrow \frac{3\times \frac{3}{2}+3}{\frac{3}{2}+1}=a\Rightarrow a=3$