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Mathematics

Two vertices of a triangle are (-5, 3) and (4, -7). If centroid of the triangle is (-1, 2) then the third vertex is :

  1. (-2, 7)

  2. (-2, 10)

  3. (-2, -10)

  4. (0, -2)

Section Formula

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Answer

Let third vertex be (x, y).

By formula,

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

Substituting values we get :

⇒(−1,2)=((−5)+4+x3,3+(−7)+y3)⇒(−1,2)=(x−13,y−43)⇒−1=x−13 and 2=y−43⇒x−1=−3 and y−4=6⇒x=−3+1 and y=6+4⇒x=−2 and y=10.\Rightarrow (-1, 2) = \Big(\dfrac{(-5) + 4 + x}{3}, \dfrac{3 + (-7) + y}{3}\Big) \\[1em] \Rightarrow (-1, 2) = \Big(\dfrac{x - 1}{3}, \dfrac{y - 4}{3}\Big) \\[1em] \Rightarrow -1 = \dfrac{x - 1}{3} \text{ and } 2 = \dfrac{y - 4}{3} \\[1em] \Rightarrow x - 1 = -3 \text{ and } y - 4 = 6 \\[1em] \Rightarrow x = -3 + 1 \text{ and } y = 6 + 4 \\[1em] \Rightarrow x = -2 \text{ and } y = 10.

Third vertex = (-2, 10).

Hence, Option 2 is the correct option.

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