To find the corresponding ordered pair at point \( A \) after the dilation of parallelogram \( ABCD \), we will use the dilation formula.
The formula for a point \( (x, y) \) that is dilated from a center of dilation \( (c_x, c_y) \) with a scale factor \( k \) is given by:
\[ (x', y') = (c_x + k \cdot (x - c_x), c_y + k \cdot (y - c_y)) \]
Given:
- Center of dilation \( (-2, -1) \)
- Scale factor \( k = 2 \)
- Original coordinates of point \( A \) (let's denote them as \( (x_A, y_A) \))
For the purpose of this calculation, let's denote the coordinates of point \( A \) as \( (x_A, y_A) \). We will apply the dilation formula to this point.
Substituting in the values, the new coordinates \( (x', y') \) will be:
\[ x' = -2 + 2 \cdot (x_A + 2) \]
\[ y' = -1 + 2 \cdot (y_A + 1) \]
This yields:
\[ x' = -2 + 2x_A + 4 = 2x_A + 2 \]
\[ y' = -1 + 2y_A + 2 = 2y_A + 1 \]
Thus, the new coordinates of point \( A \) after dilation will be:
\[ (x_A', y_A') = (2x_A + 2, 2y_A + 1) \]
If you provide the specific coordinates of point \( A \), I can compute the new coordinates explicitly. Otherwise, the transformation has been defined generically.