Verified answer

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.