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Activity Discussion Math Centroid of the Triangle

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  • Centroid of the Triangle

    Posted by Ayushi on February 8, 2024 at 5:53 pm

    Find the centroid of the triangle whose vertices are the points A (8, 4) B (1, 3), and C (3, -1).

    Nitesh replied 1 week, 1 day ago 2 Members · 1 Reply
  • 1 Reply
  • Nitesh

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    February 12, 2024 at 12:54 pm
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    To find the centroid of a triangle, you need to calculate the average of the x-coordinates and the average of the y-coordinates of its vertices.

    Let’s denote the coordinates of point A as (x₁, y₁), the coordinates of point B as (x₂, y₂), and the coordinates of point C as (x₃, y₃).

    In this case, A (8, 4), B (1, 3), and C (3, -1), so we have:

    x₁ = 8, y₁ = 4
    x₂ = 1, y₂ = 3
    x₃ = 3, y₃ = -1

    To find the centroid, we calculate the average of the x-coordinates and the average of the y-coordinates:

    x̄ = (x₁ + x₂ + x₃) / 3
    ȳ = (y₁ + y₂ + y₃) / 3

    Substituting the values, we get:

    x̄ = (8 + 1 + 3) / 3 = 12 / 3 = 4
    ȳ = (4 + 3 – 1) / 3 = 6 / 3 = 2

    Therefore, the centroid of the triangle with vertices A (8, 4), B (1, 3), and C (3, -1) is located at the point (4, 2).

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