To find the coordinates of triangle A′B′C′ after translating triangle ABC by 3 units to the left and 5 units down, we need to adjust the coordinates of each vertex of triangle ABC accordingly.
Let's denote the original coordinates of points A, B, and C as \( (x_A, y_A) \), \( (x_B, y_B) \), and \( (x_C, y_C) \). The translation transforms these points as follows:
- Move 3 units to the left: This means we subtract 3 from the x-coordinates.
- Move 5 units down: This means we subtract 5 from the y-coordinates.
The new coordinates will be calculated as:
- \( A' = (x_A - 3, y_A - 5) \)
- \( B' = (x_B - 3, y_B - 5) \)
- \( C' = (x_C - 3, y_C - 5) \)
Since we do not have the original coordinates of triangle ABC provided, we cannot calculate the specific new coordinates, but we can evaluate the given response options against the translation rules.
To check each option:
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A′(−1,2), B′(−3,−2), C′(2,0): We cannot verify without original coordinates.
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A′(1,0), B′(−1,−4), C′(4,−2): We cannot verify without original coordinates.
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A′(7,0), B′(5,−4), C′(10,−2): We cannot verify without original coordinates.
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A′(1,10), B′(−1,6), C′(4,7): We cannot verify without original coordinates.
To find the correct response, you would need to know the original positions of A, B, and C. If you input those original coordinates, we could then calculate the new positions and identify the correct option. Without the original coordinates, we cannot determine which option is correct. Please provide the original coordinates if available.