Question
In triangle ABC, vertices are A(2, 3), B(8, 5) and C(4,
−1). Find the coordinates of the centroid and the length of the median from A.Solution
Centroid G = ((x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3) x-coordinate = (2 + 8 + 4)/3 = 14/3 y-coordinate = (3 + 5 − 1)/3 = 7/3 So G(14/3, 7/3) Median from A joins A(2,3) to midpoint of BC. Midpoint of BC: B(8,5), C(4,−1) M = ((8+4)/2, (5−1)/2) = (12/2, 4/2) = (6,2) Length AM = √[(6 − 2)² + (2 − 3)²] = √[(4)² + (−1)²] = √(16 + 1) = √17.
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