Question

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

Since, $AC=2BC$

$\frac{AC}{BC}=\frac{2}{1}$

Point $C$ divides $AB$ in the $2:1$ ratio

Giving $A(-3,4)$ and $B(2,1)$

Here we apply the section formula, i. e. 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

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

$\therefore$ Coordinate of $C$ are

$(\frac{4-3}{2+1},\frac{2+4}{2+1})$ ie, $(\frac{1}{3},2)$