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**Goal: to rotate a figure around a central point**

Transformations Goal: to rotate a figure around a central point

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**Transformations and rotations**

Transformation refers to any copy of a geometric figure, similar to copying and pasting on your computer. A Rotation is a type of transformation where the geometric figure is spun around a fixed point known as the “center of rotation”. Rotations can be made “clockwise” and “counterclockwise”. Common rotations are 45, 90, 180, and 270 degrees. Rotation A to A’ 90 degrees counter clockwise

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**Rotation by 180° about the origin: R(origin, 180°)**

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Graphing Rotations The easiest way to think about rotations is to first think of a single coordinate rotation. 1. Graph the point (1,2) on your paper. 2. Rotate this point 90 degrees clockwise by first drawing a straight line to the “origin”. 3. Secondly, draw a straight line from the origin down and to the right in order to form a right angle. 4. Your second point should fall at (2,-1).

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180-degree rotation 1. From the same point (1,2), draw a straight line through the origin. 2. The point that your line hits that is equidistance from (1,2) is your 180-degree clockwise rotation. 3. Your second point should fall at (-1,-2)

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270-degree rotation 1. Start from (1,2), draw a straight line through the origin until you hit (-1,-2). 2. This is 180 degrees from the last example. 3. We must add 90 degrees to this. 4. Draw another line from the origin up and to the left to make a 90-degree angle between (-1,-2), the origin, and a last point. 5. This point should fall on (-2,1).

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RULE: A rotated object’s vertices will form an angle with its original object’s vertices equal to the degree measure of the rotation. The above rotation shows 90-degree angles between all rotated vertices.

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**Example 2: 180-degree rotation**

All of the vertices of the triangle on the left are rotated 180 degrees through the center of reflection.

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Practice!!!!

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Warm Up Draw an example of a reflection: Draw an example of a figure that has one or more lines of symmetry: Find the new coordinates of the image after.

Warm Up Draw an example of a reflection: Draw an example of a figure that has one or more lines of symmetry: Find the new coordinates of the image after.

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