Question

If the coordinates of the points $A$ and $B$ in a plane are $(1,1)$ and $(1,2)$ respectively, find the
coordinates of $C$ (in the plane) such that $\overrightarrow{AB}$ and $\overrightarrow{BC}$ are equal.

Answer 1

Let $C=(x,y)$

$\because \overrightarrow{AB}=\overrightarrow{BC}$ so

$x-1=0$

$\Rightarrow x=1$ & $y-2=1$

$y=3$

$\overrightarrow{AB}=\hat{j}$

$\overrightarrow{BC}=(x-1)\hat{i}+(y-2)\hat{j}$

so $C=(1,3)$