Question

$A(1,1)$ and $B(2,-3)$ two points and $D$ is a point on $AB$ produced such $AD=3AB$. Find the co-ordinates of $D$.

Answer 1

Given $AD=3AB$.

$AB+BD=3AB$

$2AB=BD$

B divides $AD$ in ratio $1:2$

Let D be $(x,y)$

$2=\frac{x+2}{3}\to x=4$

$-3=\frac{y+2}{3}\to y=-11$

$\therefore D(4,-11)$