A triangle has a vertex at ( 1 ,   2 ) and the mid points of the two sides through it are ( - 1 , &#160…

1. $\left(\frac{1}{3},1\right)$
2. $\left(1, \frac{7}{3}\right)$
3. $\left(\frac{1}{3}, 2\right)$
4. $\left(\frac{1}{3}, \frac{5}{3}\right)$

Solution

Let co-ordinates of $B=\left(x_1,y_1\right)$
$\therefore \frac{x_1+1}{2}= -1 \& \frac{y_1+2 }{2}=1$
$\Rightarrow x_1=-3, y_1=0$
$\therefore B=(-3, 0)$
Let co-ordinates of $C=\left(x_2,y_2\right)$
$\therefore \frac{x_2+1}{2}=2 \& \frac{y_2+2}{2}=3$
$\therefore C=\left(3, 4\right)$
Let centroid $G=\left(h,k\right)$
$h=\frac{1+x_1+x_2}{3}=\frac{1-3+3}{3}=\frac{1}{3}$
$k=\frac{2+y_1+y_2}{3}=\frac{2+0+4}{3}=2$
$\therefore \mathrm{ }\mathrm{ }$ Centroid, $\mathrm{G}=\left(\frac{1}{3},2\right)$

Asked in: JEE Main 2019 (12 Apr Shift 2)

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