Answer:
To find the coordinates of the vertices of triangle BCD after it is scaled by a factor of 3, centered at the origin, you would first need to find the coordinates of the vertices of the triangle when it is centered at the origin. This can be done by subtracting the coordinates of the original centroid, which is the point (3.33, -0.66) for triangle BCD, from the coordinates of each vertex. So the coordinates of vertex B would be (2 - 3.33, -1 + 0.66) = (-1.33, -0.34), the coordinates of vertex C would be (4 - 3.33, 1 - 0.66) = (0.67, 0.34), and the coordinates of vertex D would be (5 - 3.33, -2 + 0.66) = (1.67, -1.34).
To scale the triangle by a factor of 3, you would multiply the coordinates of each vertex by 3. So the coordinates of the scaled triangle would be (-3.99, -1.02) for vertex B, (2.01, 1.02) for vertex C, and (5.01, -4.02) for vertex D.
Therefore, the coordinates of the vertices of triangle BCD after it is scaled by a factor of 3, centered at the origin, would be (-3.99, -1.02), (2.01, 1.02), and (5.01, -4.02).