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Q.
If two vertices of a triangle are $(-1,4)$ and $(5,2)$ and its centroid is $(0,-3)$, then the third vertex is
Straight Lines
Solution:
Let the third vertex be $(x, y)$. Then, the coordinates of the centroid of triangle are
$\left(\frac{-1+5+x}{3}, \frac{4+2+y}{3}\right) \text { i.e., }\left(\frac{4+x}{3}, \frac{6+y}{3}\right) \text {. }$
Now, $\left(\frac{4+x}{3}, \frac{6+y}{3}\right)=(0,-3)$
$\Rightarrow \frac{4+x}{3}=0 $ and $ \frac{6+y}{3}=-3 $
$\Rightarrow 4+x=0 $ and $ y+6=-9$
or $ x=-4 $ and $ y=-15$
Hence, the third vertex is $(-4,-15)$.