Question

In a triangle $ABC$, co-ordinates of $A$ are $(1,2)$ and the equations to the medians through $B$ and $C$ are $x+y=5$ and $x=4$ respectively. Then the co-ordinates of $B$ and $C$ will be

• A. $(-2,7),(4,3)$
• B. $(7,-2),(4,3)$
• C. $(2,7),(-4,3)$
• D. $(2,-7),(3,-4)$

Answer 1

Answer: (B)

$x_1+y_1=\mathrm{5....}$(i)
$x_2=\mathrm{4.....}$(ii)
co - ordinates of $G$ are $\equiv (4,1)$
$\Rightarrow \frac{1+x_1+x_2}{3}=\mathrm{4......}$(iii)
and $\frac{y_1+y_2+2}{3}=\mathrm{1.....}$(iv)
solving above equations, we get $B$ \& $C$.