If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2) , then the centroid of the triangle is: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (- 1, 2) and (3, 2), then the centroid of the triangle is:

Solution & Step-by-step Explanation

Let vertex A = (1, 1) . Let B = (x_{2}, y_{2}) and C = (x_{3}, y_{3}) .Midpoint of A B : (\frac{1 + x _{2}}{2}, \frac{1 + y _{2}}{2}) = (- 1, 2) . 1 + x_{2} = - 2 ⟹ x_{2} = - 3 1 + y_{2} = 4 ⟹ y_{2} = 3 So B = (- 3, 3) .Midpoint of A C : (\frac{1 + x _{3}}{2}, \frac{1 + y _{3}}{2}) = (3, 2) . 1 + x_{3} = 6 ⟹ x_{3} = 5 1 + y_{3} = 4 ⟹ y_{3} = 3 So C = (5, 3) .Centroid G : G = (\frac{1 + ( - 3 ) + 5}{3}, \frac{1 + 3 + 3}{3}) = (\frac{3}{3}, \frac{7}{3}) = (1, 7/3)

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If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (- 1, 2) and (3, 2), then the centroid of the triangle is:

(- 1, 7/3)

(- 1/3, 7/3)

(1, 7/3)

(1/3, 7/3)

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