Question
The vertices of triangle ABC are A(1, 4), B(5, 2) and
C(7, 8). Find the coordinates of the centroid and the length of median from A.Solution
Centroid G = ((x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3) x-coordinate: (1 + 5 + 7)/3 = 13/3 y-coordinate: (4 + 2 + 8)/3 = 14/3 So G(13/3, 14/3) Length of median from A is AG: A(1, 4), G(13/3, 14/3) AG = √[(13/3 − 1)² + (14/3 − 4)²] = √[(10/3)² + (2/3)²] = √[(100/9) + (4/9)] = √(104/9) = (1/3)√104 = (2/3)√26.
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