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EXPLANATION.
Circumcentre of the triangle formed by (9,3), (-1,7) & (-1,3).
As we know that,
Let,
⇒ A = (9,3).
⇒ B = (-1,7).
⇒ C = (-1,3).
Circumcentre (x) = Midpoint of AB.
⇒ x = (9 - 1)/2 , (3 + 7)/2.
⇒ x = 4, 5.
Centroid of a triangle = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3.
⇒ (9 + (-1) + (-1))/3 , (3 + 7 + 3)/3.
⇒ (9 - 1 - 1)/3 , (3 + 7 + 3)/3.
⇒ (7/3) , (13/3).
Centroid of a triangle in new system = (x - h, y - k).
⇒ (7/3 - 4) , (13/3 - 5).
⇒ (7 - 12/3) , (13 - 15/3).
⇒ (-5/3), (-2/3).
Option [C] is correct answer.
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