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If G(-2, 1) is the centroid of a ΔABC and two of its vertices are A(1, -6) and B(-5, 2) , find the third vertex of the triangle.

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#### Solution

Two vertices of ΔABC are A(1, -6) and B(-5, 2) Let the third vertex be C(a, b). Then the coordinates of its centroid are

`c ((1-5+a)/3,(-6+2+b)/3)`

`c((-4+a)/3,(-4+b)/3)`

But it is given that G (-2.1) is the centroid. Therefore,

`-2 = (-4+a)/3, 1=(-4+b)/3`

⇒ -6=-4+a,3=-4+b

⇒ -6+4= a, 3+4=b

⇒ a =-2, b=7

Therefore, the third vertex of ΔABC is C (-2,7 ).

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