To perform a dilation of a point \( D(3, 3) \) using a center of dilation at \( (1, 1) \) and a magnitude of 12, you can use the formula for dilation.
The formula for the coordinates \( (x', y') \) of the dilated point is given by:
\[ (x', y') = (x_c + k(x - x_c), y_c + k(y - y_c)) \]
where:
- \( (x_c, y_c) \) is the center of dilation,
- \( (x, y) \) is the original point,
- \( k \) is the dilation factor (magnitude).
In this case:
- \( (x_c, y_c) = (1, 1) \)
- \( (x, y) = (3, 3) \)
- \( k = 12 \)
Plugging in the values:
-
For \( x' \): \[ x' = 1 + 12(3 - 1) = 1 + 12(2) = 1 + 24 = 25 \]
-
For \( y' \): \[ y' = 1 + 12(3 - 1) = 1 + 12(2) = 1 + 24 = 25 \]
Thus, the new coordinates after dilation are \( (25, 25) \).
So, the corresponding ordered pair to the current point \( D \) after dilation is \( (25, 25) \).