To determine the new coordinates of a figure when it is rotated 180° clockwise about the origin, we can apply the transformation rule for a 180° rotation. This transformation negates both the x and y coordinates of each point.
Given a point \( (x, y) \), rotating it 180° about the origin results in the point \( (-x, -y) \).
To find the correct answer from the options provided, we would normally need the original coordinates of points A, B, and C. However, since they are not provided, we can assess the transformations of the coordinates listed in each option.
Let's apply the transformation to check the potential new coordinates based on the following points:
- \( A(-x, -y) \)
- \( B(-x, -y) \)
- \( C(-x, -y) \)
Now let's analyze which one of the options corresponds to the 180° rotation.
- Option A: \( A'(-3,3), B'(-7,3), C'(-7,-3) \)
- Option B: \( A'(3,3), B'(-3,7), C'(3,7) \)
- Option C: \( A'(3,3), B'(3,7), C'(-3,7) \)
- Option D: \( A'(-3,3), B'(-7,3), C'(7,-3) \)
To see if any of the options might fit the rule, we can consider typical points before rotation, but since that information is not provided in this query, we have to stick to possible transformations.
If we assume the figure originally had points that were situated in positive quadrants of the Cartesian plane, then their transformations upon 180° rotation should yield negative values for both x and y, as they should land in opposite quadrants.
Checking the transformations again:
- Option A: Includes shifted points to various quadrants but not consistently negative.
- Option B: Shows positive quadrants which contradicts the negation rule.
- Option C: Also yields a mix, which does not capture the 180° rotation effectively.
- Option D: Includes a combination of different quadrants but retains some symmetry.
If we strictly apply the transformation and since we lack the original coordinates, we cannot definitively select which one is correct without them. However, based on typical expectations from a rotation:
- Rotation should yield negative signs across the board when dealing with positions likely in the first two quadrants. That could suggest either option A or D might be more valid.
Thus, without original coordinates shared for confirmation, we'd need to know the figure's starting positions. Selecting the most consistently transformed option leans towards D for its variety.
Therefore, based on that conceptual validation:
Final answer: D. A'(-3,3), B'(-7,3), C'(7,-3) but keep aware that accurate coordinates define the solution best!