Name Date. Go to BigIdeasMath.com for an interactive tool to investigate this exploration. and those of A BC?

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1 ame Date.3 Rotations For use with Eploration.3 Essential Question How can ou rotate a figure in a coordinate plane? EXPLORTIO: Rotating a Triangle in a oordinate Plane Go to igideasath.com for an interactive tool to investigate this eploration. a. Use dnamic geometr software to draw an triangle and label it. b. Rotate the triangle 90 counterclockwise about the origin to form. c. What is the relationship between the coordinates of the vertices of and those of? d. What do ou observe about the side lengths and angle measures of the two triangles? 2 EXPLORTIO: Rotating a Triangle in a oordinate Plane Go to igideasath.com for an interactive tool to investigate this eploration. a. The point (, ) is rotated 90 counterclockwise about the origin. Write a rule to determine the coordinates of the image of (, ). b. Use the rule ou wrote in part (a) to rotate 90 counterclockwise about the origin. What are the coordinates of the vertices of the image,? 5 5 c. Draw. re its side lengths the same as those of? Justif our answer. 02 Geometr opright ig Ideas Learning, LL

2 ame Date.3 Rotations (continued) 3 EXPLORTIO: Rotating a Triangle in a oordinate Plane a. The point (, ) is rotated 80 counterclockwise about the origin. Write a rule to determine the coordinates of the image of (, ). Eplain how ou found the rule. b. Use the rule ou wrote in part (a) to rotate 80 counterclockwise about the origin. What are the coordinates of the vertices of the image,? 5 5 ommunicate Your nswer. How can ou rotate a figure in a coordinate plane? 5. In Eploration 3, rotate 80 counterclockwise about the origin. What are the coordinates of the vertices of the image,? How are these coordinates related to the coordinates of the vertices of the original triangle,? opright ig Ideas Learning, LL Geometr 03

3 ame Date.3 otetaking with Vocabular For use after Lesson.3 In our own words, write the meaning of each vocabular term. center of angle of al smmetr center of smmetr ore oncepts Rotations is a transformation is which a figure is turned about a fied point called the center of. Ras drawn from the center of to a point and its image form the angle of. about a point P through an angle of maps ever point Q in the plane to a point Q, so that one of the following properties is true. If Q is not the center of P, then QP = Q P and m QPQ =, or If Q is the center of P, then Q = Q. R Q center of 0 R Q angle of P otes: 0 Geometr opright ig Ideas Learning, LL

4 ame Date.3 otetaking with Vocabular (continued) oordinate Rules for Rotations about the Origin When a point ( a, b) is rotated counterclockwise about the origin, the following are true. For a of ( a b) ( b a) 90,,,. For a of ( a b) ( a b) 80,,,. For a of ( a b) ( b a) otes: 270,,,. ( b, a) ( a, b) (a, b) (b, a) Postulate.3 Rotation Postulate is a rigid motion. Etra Practice In Eercises 3, graph the image of the polgon after a of the given number of degrees about the origin J K L T R S D In Eercises 7, graph the image of after the composition.. Reflection: -ais 5. Rotation: 90 about the origin Rotation: 80 about the origin Translation: (, ) ( + 2, 3) opright ig Ideas Learning, LL Geometr 05

5 ame Date.3 otetaking with Vocabular (continued) 6. Rotation: 270 about the origin 7. Rotation: 90 about the origin Reflection: in the line = Translation: (, ) ( 5, ) In Eercises 8 and 9, graph JKL its image after the composition. with vertices J( 2, 3 ), K(, ), and L(, 0) and 8. Rotation: 80 about the origin 9. Translation: (, ) (, ) Reflection: = 2 Rotation: 270 about the origin In Eercises 0 and, determine whether the figure has al smmetr. If so, describe an s that map the figure onto itself Geometr opright ig Ideas Learning, LL