Question

In a $△ABC$, co-ordinates of orthocentre, centroid and vertex $A$ are $(3,2),(3,1)$ and $(1,2)$ respectively. Then $x-$coordinate of vertex $B$ is

Answer 1

$A$ is parallel to $x-$axis

As $C\perp AH$ produced

$\Rightarrow BC$ is parallel to $y-$axis

$\Rightarrow B$ and $C$ have same $x-$coordinates

As $x-$coordinates of $G=\frac{1+a+a}{3}$

$\Rightarrow 3=\frac{1+2a}{3}\Rightarrow 2a=9\Rightarrow a=4$

$\Rightarrow a=4$