Question

Find the centroid of the triangle whose vertices are (a, b), (2a,2b),(3a,3b)​

Answer 1

the centroid is (2a ,2b)

Answer 2

we have to find the centroid of the triangle whose vertices are (a, b), (2a, 2b) and (3a, 3b).

solution : the centroid of a triangle is the point of intersection of the medians of the triangle.

if (x₁ , y₁) , (x₂ , y₂) and (x₃ , y₃) are the vertices of a triangle then centroid of this triangle is given by, [(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3]

so centroid of the triangle whose vertices are (a,b), (2a, 2b) and (3a , 3b) is given by,

= [(a + 2a + 3a)/3 , (b + 2b + 3b)/3]

= (6a/3, 6b/3)

= (2a , 2b)

Therefore the centroid of the given triangle is (2a, 2b).

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