To rotate a point 180° counterclockwise around another point, you can use the following method:
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Determine the center of rotation and the point to be rotated.
- Center of rotation: \((-4, 6)\)
- Point to rotate: \((-4, 6)\)
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Compute the resulting point after a 180° rotation. The formula for rotating a point \((x, y)\) around another point \((h, k)\) by 180° is: \[ (h - (x - h), k - (y - k)) \]
Since our point to rotate is the same as the center of rotation, the calculation becomes: \[ (-4 - (−4 - (−4)), 6 - (6 - 6)) = (-4, 6) \]
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Resulting point: Since the point is the same as the rotation center, it remains \((-4, 6)\).
However, if you intended to rotate any other point around \((-4, 6)\), you would follow this procedure with your specific coordinates.
Since none of the responses match the input point or reasoning, please clarify the original point to be rotated if it's not \((-4, 6)\). The prompt seems to imply a misunderstanding, because specifying the rotation and the point to be rotated is crucial.
If you're looking for a general rotation of a point, could you please provide the point again?