To dilate a figure with a magnitude of \( k \) in reference to the origin, you multiply each coordinate of the vertices by \( k \).
Given the dilation magnitude of \( 3 \), if a triangle has original vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), then the new vertices after dilation will be:
\[ A' = (3x_1, 3y_1) \] \[ B' = (3x_2, 3y_2) \] \[ C' = (3x_3, 3y_3) \]
It's important to know the original coordinates of the triangle's vertices to find the new coordinates after dilation. Since the original coordinates of the triangle are not provided in your message, I can't directly calculate the new coordinates.
However, based on the given options, you can verify which set of coordinates forms valid \( A', B', C' \) vertices when the original coordinates are multiplied by \( 3 \).
If you provide the original coordinates, I can perform the multiplication and help identify the correct responses from the options provided.
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