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Mathematics

The centroid of triangle ABC is G = (6, -3). If A = (-6, -3), B = (x, 6) and C = (9, y), then the values of x and y are :

  1. x = 6, y = 15

  2. x = 15, y = -12

  3. x = 15, y = 6

  4. x = -15, y = 6

Straight Line Eq

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Answer

By formula,

Centroid of triangle = (x1+x2+x33,y1+y2+y33)\Big(\dfrac{x1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3}\Big)

Since, G is the centroid of triangle ABC.

Substituting values we get :

⇒(6,−3)=(−6+x+93,−3+6+y3)⇒(6,−3)=(x+33,y+33)⇒x+33=6 and y+33=−3⇒x+3=18 and y+3=−9⇒x=18−3 and y=−9−3⇒x=15 and y=−12.\Rightarrow (6, -3) = \Big(\dfrac{-6 + x + 9}{3}, \dfrac{-3 + 6 + y}{3}\Big) \\[1em] \Rightarrow (6, -3) = \Big(\dfrac{x + 3}{3}, \dfrac{y + 3}{3}\Big) \\[1em] \Rightarrow \dfrac{x + 3}{3} = 6 \text{ and } \dfrac{y + 3}{3} = -3 \\[1em] \Rightarrow x + 3 = 18 \text{ and } y + 3 = -9 \\[1em] \Rightarrow x = 18 - 3 \text{ and } y = -9 - 3 \\[1em] \Rightarrow x = 15 \text{ and } y = -12.

Hence, Option 2 is the correct option.

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