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## Isometries

Symmetries are one of the most beautiful part of Geometry. Slide into reflections, rotations, translations, and more, and you'll be on your way to geometric artistry.

# Rotation

If the point $$(3, 11)$$ is rotated $$90^\circ$$ counterclockwise about the origin, what are the coordinates of the new point?

If the point $$(6, 3)$$ is rotated $$180^\circ$$ counterclockwise about $$(2,9),$$ what are the coordinates of the new point?

If the point $$(2, 9)$$ is rotated $$90^\circ$$ counterclockwise about $$(1,1),$$ what are the coordinates of the new point?

After counterclockwise rotation by $$270^\circ$$ about $$(1, 2),$$ the coordinates of the point changes by $$(5, 4).$$ What is the point before rotation?

If the point $$(8, 3)$$ is rotated $$270^\circ$$ counterclockwise about the origin, what are the coordinates of the new point?

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