If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =

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We have to find the unknown co-ordinates. The co-ordinates of vertices are A(7, x) ; B(y , -6) ; C(9,10) The co-ordinate of the centroid is (6, 3) We know that the co-ordinates of the centroid of a triangle whose vertices are `(x_1 ,y_1) ,(x_2 , y_2) ,(x_3 ,y_3) is ((x_1 + x_2 + x_3 )/3 , ( y_1 + y_2 + y_3)/ 3) So, (6,3) = ((y + 7 + 9) /3 , (x-6 +10)/3)` Compare individual terms on both the sides- (x +4)/3 = 3 So, x = 5 Similarly, (y + 16)/3 = 6 So, y = 2

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