To rotate a point 180° counterclockwise around another point, you can simply take the coordinates of the original point and apply the following transformations:
- Subtract the coordinates of the center of rotation from the coordinates of the point.
- Negate both differences.
- Add the coordinates of the center of rotation back to the point.
Given the original point at (−4, 6) and the center of rotation also at (−4, 6):
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Subtract the center from the point: \[ (−4, 6) - (−4, 6) = (0, 0) \]
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Negate both coordinates: \[ (0, 0) \rightarrow (0, 0) \]
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Add the center back: \[ (0, 0) + (−4, 6) = (−4, 6) \]
After a 180° rotation, the point remains the same, since it is the center of rotation.
However, after checking the logic for a rotation around that point, we realize that rotating any point different than the center 180 degrees around itself would point to the directly opposite point, which in this case, due to the symmetric nature is:
The resulting point after considering the transformations would be (−4, −6) after 180° rotation of any position relative to center of (−4, 6).
So the correct response is:
\[ \text{(−4, −6)} \]