The rotation that will carry a regular hexagon onto itself is 90 degree counterclockwise rotation.
How does rotation by 90 degrees changes the coordinates of a point if rotation is with respect to origin?
Let the point be having coordinates (x,y).
Case 1: If the point is in the first quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 2: If the point is in the second quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 3: If the point is in third quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 4: If the point is in fourth quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 5: For points on axes
You can take that point in any of the two surrounding quadrants. Example, if the point is on positive x axis, then it can taken as of first quadrant or fourth quadrant.
Case 6: On the origin
No effect as we assumed rotation is being with respect to the origin.
The rotation that will carry a regular hexagon onto itself is 90 degree counterclockwise rotation.
Learn more about the rotation of a point with respect to origin here:
https://brainly.com/question/18856342
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