To translate triangle ABC by 3 units to the left and 5 units down, you can follow these steps:
- Translation to the left by 3 units means you subtract 3 from the x-coordinates of each vertex.
- Translation down by 5 units means you subtract 5 from the y-coordinates of each vertex.
If we denote the original coordinates of points A, B, and C as \( A(x_A, y_A) \), \( B(x_B, y_B) \), and \( C(x_C, y_C) \), the new coordinates after translation would be:
- \( A'(x_A - 3, y_A - 5) \)
- \( B'(x_B - 3, y_B - 5) \)
- \( C'(x_C - 3, y_C - 5) \)
However, since we don't have the original coordinates given, we need to evaluate the given responses as potentially translated points.
Let's analyze each of the options based on the expected transformation.
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Option 1: A′(7,0), B′(5,−4), C′(10,−2)
- These points are not possible since they appear to be to the right (positive x) and have no relation to a leftward shift.
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Option 2: A′(−1,2), B′(−3,−2), C′(2,0)
- These points might represent a shift but again do not account for any specific points.
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Option 3: A′(1,0), B′(−1,−4), C′(4,−2)
- This set of points falls into a range indicative of movement, but again with no specific original points to compare.
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Option 4: A′(1,10), B′(−1,6), C′(4,7)
- Similar to the other sets but remains higher in y-coordinates which would suggest no downward shift occurred.
Since we don't have the original triangle's coordinates, we should rely on which set of transformed points seems most reasonable given a standard movement scenario across a range. Identifying logical coordinates after such movements typically would implicate options 2 and 3 are the most plausible considering their applicable negative movements in y-coordinates.
Notably, a final selection based on general observation and the rules of coordinate transformations would indicate option 3: A′(1,0), B′(−1,−4), C′(4,−2) as most indicative of a leftward and downward translation consistent with mathematical expectations of triangular coordinates.