Question

If $C$ is a point on the line segment joining $A\left(-3,4\right)$ and $B\left(2,1\right)$ such that $AC=2BC,$ then the coordinate of $C$ is

• A. $\left(\frac{1}{3},2\right)$
• B. $\left(2,\frac{1}{3}\right)$
• C. $\left(2,7\right)$
• D. $\left(7,2\right)$

Answer 1

The correct option is A

$\left(\frac{1}{3},2\right)$

Explanation for the correct options:

Finding the value of coordinate $C$:

Given that $C$ is the point divides the line segment $AB$ in the ratio of $2:1$

By using section formula, we get

$\Rightarrow x=\frac{\left[2\left(2\right)+1\left(-3\right)\right]}{2+1}$

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

$\Rightarrow y=\frac{\left[2\left(1\right)+1\left(4\right)\right]}{2+1}$

$\Rightarrow y=2$

$\Rightarrow C=\left(\frac{1}{3},2\right)$

Hence, option (A) is correct.