Question

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

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

Answer 1

The correct option is A $(\frac{1}{3},2)$

Here we apply the section formula: If a point $C(x,y)$ divides the line segment $AB$ joining the points $A(x_1,y_1)\&B(x_2,y_2)$ in the ratio $m:n$ then we have

$x=\frac{n{x}_1+m{x}_2}{m+n}\&y=\frac{n{y}_1+m{y}_2}{m+n}.$

Let the point is C( $x,y$), Which divides AB in the ratio of $2:1$.

Then the coordinates of C are given by

$x=\frac{(2\times 2)+(-3\times 1)}{2+1}=\frac{1}{3}$

$y=\frac{(2\times 1)+(1\times 4)}{3}=2$

$C\equiv (\frac{1}{3},2)$