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    Question

    The vertices of triangle ABC are A(1, 4), B(5, 2) and

    C(7, 8). Find the coordinates of the centroid and the length of median from A.
    A (1/3)√2 Correct Answer Incorrect Answer
    B (2/3)√26 Correct Answer Incorrect Answer
    C (2/7)√29 Correct Answer Incorrect Answer
    D (5/3)√20 Correct Answer Incorrect Answer

    Solution

    Centroid G = ((x₁ + xβ‚‚ + x₃)/3 , (y₁ + yβ‚‚ + y₃)/3) x-coordinate: (1 + 5 + 7)/3 = 13/3 y-coordinate: (4 + 2 + 8)/3 = 14/3 So G(13/3, 14/3) Length of median from A is AG: A(1, 4), G(13/3, 14/3) AG = √[(13/3 βˆ’ 1)Β² + (14/3 βˆ’ 4)Β²] = √[(10/3)Β² + (2/3)Β²] = √[(100/9) + (4/9)] = √(104/9) = (1/3)√104 = (2/3)√26.

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