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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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