# 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. - Mathematics

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.

#### 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 ).

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 22