Question

Find the co-ordinates of a point C on AB produced such that $3AB=AC$, where $A=(3,2)$ and $B=(-2,4).$

• A. $(-12,8)$
• B. $(8,12)$
• C. $(12,8)$
• D. $(-8,12)$

Answer 1

The correct option is A $(-12,8)$

From the above condition, we can observe that the point B divides the line segment joining AC in 1;3 ratio, or $AC:AB=3:1$ or $AB:BC=2:1$. Let the coordinates of C be (x,y). Therefore,
$B(-2,4)=(\frac{1\left(x\right)+2\left(3\right)}{3},\frac{1\left(y\right)+2\left(2\right)}{3})$
Or $\frac{6+x}{3}=-2$ or $6+x=-6$ or $x=-12$. Similarly $\frac{4+y}{3}=4$ or $4+y=12$ or $y=8$.
Hence $C(x,y)=(-12,8)$