A rotation is a transformation that turns a figure around a point, called the.

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1 Name: # Geometr: Period Ms. Pierre Date: Rotations Toda s Objective KWBAT represent a rotation as a function of coordinate pairs and rotate a figure in the plane following a rule described in words or as a function. A circle is the set of all points that are the same distance from a point called the center. Visualize turning the circle shown on the right so that point A moves onto point B. If ou did that, the points would remain the same distance from the center, but the would be in a different location. A rotation is a transformation that turns a figure around a point, called the. Just as with points on a circle, when ou rotate a point around a center of rotation, it remains the same distance from the center of rotation. You can rotate a figure an number of degrees. Counterclockwise is considered the positive direction, so the rotation shown below would be described as 5 rotation around the origin. The same image could be obtained, however, b rotating the figure 315 clockwise, since 30 5 = 315. So, this rotation could also be called a 315 rotation around the origin.

2 You can represent a rotation as a function for which the input is a coordinate pair. The output of that function is the image produced b the rotation. A 90 rotation is equivalent to a rotation and has the function: R,-, = A 180 rotation is equivalent to a rotation and has the function: R 3-, = A 70 rotation is equivalent to a rotation and has the function: R 78-, = Write true or false for each statement. If false, rewrite the statement to make it true. 1. A circle is the set of all points that are equidistant from a point called the center.. A quarter-turn in the counterclockwise direction is equivalent to a 90 rotation.

3 Eample 1 Triangle GHJ is graphed on the coordinate plane. Draw the image of this triangle after counterclockwise rotations of 90, 180, and 70 about the origin. dinate plane. Draw the image of rotations of 90, 180, and 70 H G 0 J n Step 1: Identif the coordinates of the vertices of GHJ. (, ), The vertices are G (1, ), H (, ), and J (, ). Step : Use the circle technique to determine the new vertices after the R,- 1, = (, ) R,- (, ) = (, ) R,- (, ) = (, ) Step 3: Use the circle technique to determine the new vertices after the counterclockwise rotation. Graph and label each image. R 3-1, = (, ) Plot the vertices of each image, label them, R 3- (, ) = (, ) and connect them. R 3- (, ) = (, ) H J H

4 Step : Use the circle technique to determine the new vertices after the R 78-1, = (, ) RIGH Step 5: Graph and label each image. H 0 G J

5 þ Check Draw for each Understanding reflected image as described and name its vertices. Identif vertices of the image. Triangle ABC is graphed on the coordinate plane. Draw the image of this triangle after 1. counterclockwise Reflect ABC rotations across the of -ais. 90, 180, and 70 about. the Reflect pentagon origin. 3. B C A 0 H J G L K Step 1: Identif the A ( coordinates, ) B ( of, the vertices ) C (, of ABC. ) G (, ) H ( The vertices are A ( REMEMBER, ) When, B a ( point is, ), and C (, ). reflected across the -ais, the K (, ) L ( sign of its -coordinate changes. Step : Use the circle technique to determine the new vertices after the Fill in each blank with an appropriate word or phrase. R,- (, ) = (, ) 3. A reflection results in R,- (, ) = (, ) two figures that look like RIGH. Lines that meet and form right angles are called li R,- (, ) = (, ) 5. A point and its reflection are each the same distance from Step 3: Use. the circle The path technique that a point to determine takes across the the new line vertices of reflection after is the counterclockwise reflection. rotation. R 3- ( Use, ) the = given ( function, ) to transform DEF. Then describe the transform R 3- ( 7., ) R(, = ) ( (,, ) ) 8. R(, ) (, ) R 3- (, ) = (, ) D D

6 Fill in each blank with an appropriate word or phrase. Step : Use the circle technique to determine the new vertices after the R 78-1, = (, ) Step 5: Graph and label each image.. B C A 0 A (, ) B (, ) C (, ) REMEMBER When a point is reflected across the -ais, the sign of its -coordinate changes.

7 Independent Practice 1.) Triangle KLM is graphed on the coordinate plane. Draw the image of this triangle after counterclockwise rotations of 70 about the origin. Step 1: Identif the coordinates of the vertices of ABC. The vertices are K (, ), L (, ), and M (, ). Step : Use the circle technique to determine the new vertices after the RIGH Step 5: Graph and label the image.

8 REMEMBER A 90 rotation is equal to a 70 rotation. Homework. Use the given function to rotate KLM to form K9L9M9. Identif the coordinates of the vertices of the image. Then identif the degree measure of the rotation R (, ) (, ) 9.. R (, ) (, ) D E L F F D 0 F L E Words: 0 K M Words: K 0 M Function: Function: Write true or false for each statement. If false, rewrite the statement to make it true. K (, ) L (, ) M (, ) K (, ) L (, ) M (, ) 5. A circle is the set of all points that are equidistant from a point called the center.. A quarter-turn in the counterclockwise direction is equivalent to a 90 rotation. 7. Corresponding sides of a preimage and an image after a 70 rotation are parallel. 30 Unit 1: Congruence, Proof, and Constructions T10NA_GEO_SE_U1_Final.indd 30 18/07/15 7:0 PM