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Triangle analytical geometry

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Triangle - centroid co-ordinates and area

Centroid of Triangle

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

xs = (x1 + x2 + x3) / 3                        (1)

ys = (y1 + y2 + y3) / 3                        (1b)

Area of Triangle

The area of the triangle can be expressed as

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

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Example - Centroid and Area of Triangle

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

xs = (0 + 1 + 1) / 3

    = 0.67

ys = (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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