To translate the quadrilateral \( ADCB \) 5 units to the left and 2 units down, we need to adjust the coordinates of each vertex of the quadrilateral accordingly.
The translation can be described mathematically as follows:
- For a horizontal translation to the left by 5 units, we subtract 5 from the x-coordinate.
- For a vertical translation down by 2 units, we subtract 2 from the y-coordinate.
Let's denote the original coordinates of the points \( A, D, C, \) and \( B \) as \( A(x_A, y_A), D(x_D, y_D), C(x_C, y_C), B(x_B, y_B) \).
After the translation, the new coordinates will be:
- \( A'(x_A - 5, y_A - 2) \)
- \( D'(x_D - 5, y_D - 2) \)
- \( C'(x_C - 5, y_C - 2) \)
- \( B'(x_B - 5, y_B - 2) \)
To find the new coordinates, we need the original coordinates of \( A, D, C, \) and \( B \). However, since the original coordinates are not provided in the question, we cannot perform the calculation to give specific new coordinates.
Assuming some made-up original coordinates (just for illustration purposes):
- \( A(4, 2) \)
- \( D(4, 7) \)
- \( C(9, 4) \)
- \( B(7, 1) \)
Then, applying the translation:
- \( A' = (4 - 5, 2 - 2) = (-1, 0) \)
- \( D' = (4 - 5, 7 - 2) = (-1, 5) \)
- \( C' = (9 - 5, 4 - 2) = (4, 2) \)
- \( B' = (7 - 5, 1 - 2) = (2, -1) \)
Based on this example, the new coordinates would yield \( A'(-1, 0), D'(-1, 5), C'(4, 2), B'(2, -1) \).
Among the choices provided, the correct one is: A′(−1, 0), D′(−1, 5), C′(4, 2), B′(2, −1).
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