To perform the dilation of point \( A(0,0) \) using a center of dilation at \( (3,0) \) with a magnitude of 3, we can use the dilation formula:
\[ (x', y') = \left( x_c + k(x - x_c), y_c + k(y - y_c) \right) \]
where:
- \((x, y)\) are the original coordinates of the point,
- \((x_c, y_c)\) are the coordinates of the center of dilation,
- \(k\) is the magnitude of the dilation,
- \((x', y')\) are the coordinates after dilation.
Given:
- Point \( A \) is \( (0, 0) \).
- Center of dilation \( C \) is \( (3, 0) \).
- Magnitude of dilation \( k = 3 \).
Now we can substitute in these values:
- \( x = 0 \), \( y = 0 \)
- \( x_c = 3 \), \( y_c = 0 \)
Plugging these into the formula gives us:
\[ (x', y') = \left( 3 + 3(0 - 3), 0 + 3(0 - 0) \right) \]
Calculating \( x' \):
\[ x' = 3 + 3(0 - 3) = 3 + 3(-3) = 3 - 9 = -6 \]
Calculating \( y' \):
\[ y' = 0 + 3(0 - 0) = 0 + 3(0) = 0 \]
Thus, the corresponding ordered pair for point \( A \) after the dilation is:
\[ (-6, 0) \]
So the final result is:
\[ \boxed{(-6, 0)} \]