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## Rotations

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**A rotation is a transformation in which a figure is turned**about a fixed point. The fixed point is called the center of rotation. Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. The angle of rotation can be measured clockwise (CW) or counterclockwise (CCW).**Can you describe the rotation?**Is this the only way to describe the rotation?**A rotation about a point P through x°**is a transformation that maps every point Q in the plane to a point Q’, so that the following properties are true. If Q is not point P, the PQ = Q’P and m<QPQ’ = x°**Rotations about the origin**90° counterclockwise about the origin**Practice #2**Rotate ∆ABC with vertices A(2,-1) , B(4,1), and C(3,3) by 90° about the origin.**Practice #2**Rotate ∆ABC with vertices A(2,-1) , B(4,1), and C(3,3) by 180° about the origin.**Practice #3**The London Eye observation wheel has a radius of 67.5m and takes 30 minutes to make a complete rotation. A car starts at position ( 34, 59 ). What are the coordinates of the car’s location after 15 minutes? Justify your answer. Find the coordinates of the location of the observation car after 7.5 minutes.**A figure in the plane has rotational symmetry if the figure**can be mapped onto itself by a rotation of 180° or less.**Let’s extend this topic…**If lines k and m intersect at point C, then a reflection in k followed by a reflection in m is a rotation about point P. The angle of rotation is 2x°, where xis the measure of the acute or right angle formed by k and m.**Classwork and Homework**Handout 7.3A and 7.3B