Question

The ratio in which the point $\left(\frac{1}{2},6\right)$ divides the line segment joining the points $(3,5)$ and $(-7,9)$ is

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

Answer 1

Answer: (B)

$1:3$

Let $\left(\frac{1}{2},6\right)$ divide the line segment joining the points $(3,5)$ and $(-7,9)$ in the ratio of $K:1$.

Using section formula, the co-ordinate of the dividing point are given as
$x=\frac{K{x}_2+x_1}{K+1}$ and $y=\frac{K{y}_2+y_1}{K+1}$

$\Rightarrow \frac{1}{2}=\frac{K(-7)+3}{K+1}$$\Rightarrow \frac{1}{2}=\frac{-7K+3}{K+1}$

$\Rightarrow K+1=-14K+6$

$\Rightarrow 15K=5$

$\Rightarrow K=\frac{1}{3}$

$\therefore$ Ratio is $1:3$