Triangle

Triangle analytical geometry.

The centroid of a triangle in a co-ordinate system can be expressed as

x_s = (x₁ + x₂ + x₃) / 3 (1)

y_s = (y₁ + y₂ + y₃) / 3 (1b)

The area of the triangle can be expressed as

A = | ((x₁ y₂ - x₂ y₁) + (x₂ y₃ - x₃ y₂) + (x₃ y₁ - x₁ y₃)) / 2 | (2)

The centroid of a triangle with points P₁(0,0), P₂(1,1) and P₃(1,0.5) can be calculated as

x_s = (0 + 1 + 1) / 3

= 0.67

y_s = (0 + 1 + 0.5) / 3

= 0.5

The area can be calculated as

A = | ((0 1 - 1 0) + (1 0.5 - 1 1) + (1 0 - 0 0.5)) / 2 |

= 0.25

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