Question

In a $\Delta ABC,$ if $A$ is $(1,2)$ and equation of the medians through $B$ and $C$ are $x+y=5$ and $x=4$ respectively then $B$ is :

• A. $(1,4)$
• B. $(7,-2)$
• C. $(4,1)$
• D. $(-2,7)$

Answer 1

The correct option is B $(7,-2)$

Point of intersection of $x+y=5$ and $x=4$ will give the centroid of the triangle, which is $G\equiv (4,1)$

$\therefore \frac{1+b+4}{3}=4\Rightarrow b=7$

So, $B\equiv (7,-2)$