• Math

  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 3 months ago 2 Members · 1 Reply

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  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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