To translate quadrilateral ADCB 5 units to the left and 2 units down, we subtract 5 from the x-coordinates and 2 from the y-coordinates of each vertex.
Let's assume the original coordinates of points A, D, C, and B are as follows:
- A(x₁, y₁)
- D(x₂, y₂)
- C(x₃, y₃)
- B(x₄, y₄)
After translation:
- A' = (x₁ - 5, y₁ - 2)
- D' = (x₂ - 5, y₂ - 2)
- C' = (x₃ - 5, y₃ - 2)
- B' = (x₄ - 5, y₄ - 2)
Let's evaluate the provided options by applying the translation on the potential coordinates.
- A′(9,−4), D′(9,1), C′(13,−2), B′(12,−5)
- A′(9,0), D′(9,5), C′(13,2), B′(12,−1)
- A′(−1,0), D′(−1,5), C′(4,2), B′(2,−1)
- A′(−1,−4), D′(−1,1), C′(4,−2), B′(2,−5)
Without the original points, we can check if there exists a congruence among the provided options.
- In option 1, it looks like first coordinates of A and D are the same and different from C and B.
- In option 2, it has higher y-values and also same x-values for A and D.
- Option 3 features lower negative x values and positive y values.
- Option 4 shows more negative numbers for x and has a mix of positive and negative y-values.
For each vertex, the x-coordinate needs to decrease by 5 and the y-coordinate needs to decrease by 2.
If you provide the original coordinates of quadrilateral ADCB, I can help calculate the new coordinates more accurately. However, based on analyzing the responses, the transformation could align with option 4, assuming the original coordinates were \( (4, -2), (4, 3), (8, 0), (7, -3) \) for point A, D, C, and B respectively.
Thus, the most fitting option without the exact original coordinates is: A′(−1,−4), D′(−1,1), C′(4,−2), B′(2,−5).
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