Question

If $A$ & $B$ are the points $(-3,4)$ and $(2,1)$, then the coordinates of the point $C$ on produced $AB$ such that $AC=2BC$ are

• A. $(2,4)$
• B. $(3,7)$
• C. $(7,-2)$
• D. $(\frac{1}{2},\frac{5}{2})$

Answer 1

The correct option is C $(7,-2)$

Using the section formula, if a point $(x,y)$ divides the
line joining the points $(x_1,y_1)$ and $(x_2,y_2)$externally in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n})$
Since, $AC=2BC=>\frac{AC}{BC}=\frac{2}{1}$
Substituting $(x_1,y_1)=(-3,4)$ and $(x_2,y_2)=(2,1)$ and $m=2,n=1$ in the section formula, we get
$C=(\frac{2\left(2\right)-1(-3)}{2-1},\frac{2\left(1\right)-1\left(4\right)}{2-1})=(7,-2)$