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Transparency 9

Transparency 9. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 9-2b. Objective. Graph rotations on a coordinate plane. Example 9-2b. Vocabulary. Rotation. A transformation involving the turning or spinning of a figure around a fixed point.

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Transparency 9

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  1. Transparency 9 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 9-2b Objective Graph rotations on a coordinate plane

  4. Example 9-2b Vocabulary Rotation A transformation involving the turning or spinning of a figure around a fixed point

  5. Example 9-2b Vocabulary Center of rotation The fixed point a rotation of a figure turns or spins around

  6. Example 9-2b Review Vocabulary Angle of rotation The degree measure of the angle through which a figure is rotated

  7. Lesson 9 Contents Example 1Rotations in the Coordinate Plane Example 2Angle of Rotation

  8. Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1a Plot the 3 coordinates R Label Q Q(1, 1) Label R R(3, 4) Q S Label S S(4, 1) Connect the dots in order that was plotted Now the fun begins! 1/2

  9. Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1a 1800 is half of a circle R Q S 1800 is a straight line Let’s use the straight line definition of 1800 1/2

  10. Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1a Since the rotation is 1800 we will be plotting the image in the opposite quadrant as the original R Q S Begin with Q(1,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0) Q’ Label Q’ 1/2

  11. Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1a Begin with R(3, 4) and draw a straight line into the opposite quadrant by passing through the origin (0, 0) R Q S Label R’ Q’ R’ 1/2

  12. Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1a Begin with S(4,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0) R Q S Label S’ S’ Q’ Connect the dots in order R’ 1/2

  13. Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1a Q’(-1, -1) R R’(-3, -4) S’(-4, -1) Q S Note: Since plotted in opposite quadrant then the numbers are the same just opposite signs S’ Q’ Answer: Must have the graph AND the coordinates R’ 1/2

  14. Graph with vertices A(4, 1), B(2, 1), and C(2, 4). Then graph the image of after a rotation of counterclockwise about the origin, and write the coordinates of its vertices. Example 9-1b Answer: A'(–4, –1), B'(–2, –1), C'(–2, –4) 1/2

  15. Example 9-2a Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Plot the 3 coordinates Label X X(2, 2) Y X Label Y Y(4, 3) Label Z Z(3, 0) Z Connect the dots in order that was plotted 2/2

  16. Example 9-2a Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices 900 is one fourth a circle Y 900 makes a right triangle X Let’s use the right angle of 9000 Z 2/2

  17. Example 9-2a Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Begin with X and draw a line to the origin Y X X’ Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2) Z From the origin make a right angle Label X’ 2/2

  18. Example 9-2a Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Begin with Y and draw a line to the origin Y’ Y X X’ Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2) Z From the origin make a right angle Label Y’ 2/2

  19. Example 9-2a Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Begin with Z and draw a line to the origin Y’ Y Z’ X X’ Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2) Z From the origin make a right angle Label Z’ 2/2

  20. Example 9-2a Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices Connect the dots in order Y’ X’(-2, 2) Y Z’ X X’ Y’(-3, 4) Z’(0, 3) Z Answer: Must have the graph AND the coordinates 2/2

  21. Example 9-1b Graph ABC with vertices A(1, 2), B(1, 4), and C(5, 5) Then graph the image of ABC after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices C C’ Answer: B A’(-2, 1) B’(-4, 1) A B’ A’ C’(-5, 5) 1/2

  22. End of Lesson 9 Assignment

  23. Example 9-2a QUILTSCopy and complete the quilt piece shown below so that the completed figure has rotational symmetry with 90°, 180°, and 270°,as its angles of rotation. 1st copy the pattern

  24. Example 9-2a Rotate the figure 90, 180, and 270 counterclockwise. Use a 90 rotation clockwise to produce the same rotation as a 270 rotation counterclockwise. 90° counterclockwise

  25. Example 9-2a Rotate the figure 90, 180, and 270 counterclockwise. Use a 90 rotation clockwise to produce the same rotation as a 270 rotation counterclockwise. 90° counterclockwise 180° counterclockwise

  26. 270° counterclockwise Example 9-2a Answer: 180° counterclockwise

  27. Example 9-2b * QUILTSCopy and complete the quilt piece shown below so that the completed figure has rotational symmetry with 90°, 180°, and 270°,as its angles of rotation.

  28. Example 9-2b Answer:

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