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  4. In a triangle A B C, 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

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Q. In a triangle $A B C$, 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

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Solution:

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