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If $G(-2,1)$ is the centroid of a $\triangle A B C$ and two of its vertices are $A(1,-6)$ and $B(-5,2)$, find the third vertex of the triangle.
If $G(-2,1)$ is the centroid of a $\triangle A B C$ and two of its vertices are $A(1,-6)$ and $B(-5,2)$, find the third vertex of the triangle.
CBSE | Class 10 | Coordinate Geometry | Exercise 16.2 | Maths | RS Aggarwal
If $G(-2,1)$ is the centroid of a $\triangle A B C$ and two of its vertices are $A(1,-6)$ and $B(-5,2)$, find the third vertex of the triangle.

Two vertices of $\triangle \mathrm{ABC}$ are $\mathrm{A}(1,-6)$ and $\mathrm{B}(-5,2)$. Let the third vertex be $\mathrm{C}(\mathrm{a}, \mathrm{b})$.

=> the coordinates of its centroid are

$C\left(\frac{1-5+a}{3}, \frac{-6+2+b}{3}\right)$

$C\left(\frac{-4+a}{3}, \frac{-4+b}{3}\right)$

But it is given that $G(-2,1)$ is the centroid. Therefore,

$-2=\frac{-4+a}{3}, 1=\frac{-4+b}{3}$

$\Rightarrow-6=-4+a, 3=-4+b$

$\Rightarrow-6+4=a, 3+4=b$

$\Rightarrow \mathrm{a}=-2, \mathrm{~b}=7$

Therefore, the third vertex of $\triangle \mathrm{ABC}$ is $C(-2,7)$.

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