To find the corresponding ordered pair for point A after dilating rectangle ABCD with a center of dilation at (3,0) and a magnitude of 3, we can use the formula for dilation:
\[ \text{Dilated Point} = \left( x_c + k(x - x_c), y_c + k(y - y_c) \right) \]
where:
- \((x, y)\) is the original point,
- \((x_c, y_c)\) is the center of dilation,
- \(k\) is the scale factor (magnitude of dilation).
For point A (0, 0):
- \((x, y) = (0, 0)\)
- \((x_c, y_c) = (3, 0)\)
- \(k = 3\)
Now we can substitute these values into the formula:
\[ \text{Dilated Point} = \left( 3 + 3(0 - 3), 0 + 3(0 - 0) \right) \]
Calculating the x-coordinate:
\[ x' = 3 + 3(0 - 3) = 3 + 3(-3) = 3 - 9 = -6 \]
Calculating the y-coordinate:
\[ y' = 0 + 3(0 - 0) = 0 + 0 = 0 \]
Thus, the corresponding ordered pair for point A after dilation is:
\[ \boxed{(-6, 0)} \]
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