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Centroid formula: find an unknown vertex or the midpoint of the opposite side

This type of question, asked 3 times: 18 Sep 2025 S1, 19 Sep 2025 S2, 21 Sep 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    18 Sep 2025 S1

    68
    Triangle ABC has its centroid at point G(4,5)G(4, 5), and vertex A is located at (2,3)(2, 3). If point D is the midpoint of side BC, what are the coordinates of D?

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  2. Question 2

    19 Sep 2025 S2

    68
    In a triangle PQR, the centroid is at G(1, 2). If the vertices P and Q are at (3, -1) and (-2, 4) respectively, what are the coordinates of vertex R?

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  3. Question 3

    21 Sep 2025 S1

    73
    In a triangle with vertices P(x, y), Q(5, -1), and R(2, 6), the Centroid is at G(4, 2). What are the coordinates of vertex P?

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