Two Vertices of a triangle ABC are given by A(6,4) and B(-2,2), and its centroid is G(3,4). Find coordinates of the third vertex C of Triangle ABC.

Given: The coordinates of two vertices of a triangle ABC are A(6, 4), B(-2, 2) and the coordinates of the centroid is 

G(3,4).

 

 

Let the coordinate of the third vertex of the triangle be C(x, y).

 

⇒ Coordinates of G = 

⇒ 4+x = 9 and  6 + y = 12

 x = 9 - 4 = 5  and  y = 12 - 6 =6

Hence, the required coordinate of the third vertex of the triangle is C(5, 6).

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As we know that

Gx=x1+x2+x3 / 3

  3 = 6 -2 +x3 /3

  9 =6 -2 +x3

 x3= 5

Gy=y1+y2+y3 / 3

4  = 4 + 2+y3 / 3

12 = 6 +y3

6 =y3

therefore the coordnate of c is (5,6)

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