Answer:

The centroid of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3) is given by the coordinates ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

In this case, A(0, 3), B(3, 6), and C(6, 9) are the vertices. Let's calculate the centroid:

Centroid coordinates = ((0 + 3 + 6)/3, (3 + 6 + 9)/3)

= (9/3, 18/3)

= (3, 6)

So, the centroid of the triangle with these vertices is (3, 6), which matches option (a).

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