Question

If $A$ and $B$ are the points $(-3,4)$ and $(2,1)$, then the co-ordinates of the point $C$ on $AB$ produced 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 $(7,-2)$

Given $AC=2BC$

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

So, C divides AB externally by $2:1$

Coordinates of $C=(\frac{m{x}_2-nx}{m-n},\frac{m{y}_2-ny}{m-n})$

where $m:n=2:1$ then $(x_1,y_1)=(-3,4)$, $(x_2,y_2)=(2,1)$

$C=(\frac{2\left(2\right)-1(-3)}{2-1},\frac{2\left(4\right)-1\left(4\right)}{2-1})$

$C=(7,-2)$