1. P ROPERTIES OF T RANSFORMATIONS

2. T RANSFORMATIONS What is a transformation? A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new image is called the image, while the original figure is called the pre-image.

3. T YPES OF T RANSFORMATIONS Translation Reflection Across a vertical line

4. Rotation Rotated about a point by a specific degree (i.e. 90 ˚ ) Dilation Reduction EnlargementAn image reduced or enlarged by a scale factor T YPES OF T RANSFORMATIONS

5. D ILATION Draw a dilation of the figure using the given scale factor. k = 2 A BC

6. D ILATION Draw a dilation of the figure using the given scale factor. k =1 1/2 A BC

7. D ILATION Draw a dilation of the figure using the given scale factor. k =1/4 A B C

8. I S THE DILATION FROM FIGURE A TO FIGURE B AN ENLARGEMENT OR REDUCTION ? F IND THE VALUES OF THE VARIABLES. A B y x 5 z 15 a 9

9. I S THE DILATION FROM FIGURE A TO FIGURE B AN ENLARGEMENT OR REDUCTION ? F IND THE VALUES OF THE VARIABLES. A B 12 1815 x y 12

10. A SSIGNMENT Practice Workbook P. 121 (1-12)

11. W HAT IS AN ISOMETRY ? A transformation that preserves original shape and size

12. T RANSLATION An object is moved or slides in a straight path A translation is an isometry. XYZ X’Y’Z’ ( x, y ) →(x + a, y + b) y x b a

13. U SE THE TRANSLATION ( X, Y ) →( X +8, Y -2) What is the image of A (10, 5)? What is the image of B (-2, 0)? What is the preimage of C’ (2, 6)? What is the preimage of D’ (-5, 0)

14. A’ A B’C’ BC T RANSLATION W RITE A RULE FOR THE TRANSLATION OF ABC TO A’B’C’. T HEN VERIFY THAT THE TRANSFORMATION IS AN ISOMETRY.

15. B CA B’ C’A’

16. 2 2 T RANSLATION T HE VERTICES OF ABC ARE A (-1,3), B (5, 0) AND C (-3, 4) G RAPH THE IMAGE OF A’B’C’. ( X, Y, ) → ( X – 2, Y + 6)

17. V ECTOR A vector is a quantity that has both direction and magnitude, or size. A vector is represented in the coordinate plane by an arrow drawn from one point to another. The component form of the vector combine the horizontal component and vertical component. The component form of AB is. B 2 units up A 3 unitsright

18. N AME THE VECTOR AND WRITE ITS COMPONENT FORM. L K

19. M N

20. U SE THE POINT P(-6, 8).F IND THE COMPONENT FORM OF THE VECTOR THAT DESCRIBES THE TRANSLATION TO P’. P’ (2, 0) P(-4, 7) P’ (-6, 2)

21. T HE VERTICES OF ABC ARE A (0, 3) B (2, 4), AND C (1, 0). T RANSLATE ABC USING THE VECTOR.

22. A SSIGNMENT Practice Workbook P. 163-164 (1-17)

23. R EFLECTIONS

24. R EFLECTION A reflection uses a line of reflection to create a mirror image of the original figure Reflection in the y axis Multiply the x coordinate by -1. (x, y) → (-x, y) Reflection in the x axis Multiply the y coordinate by -1. (x, y) →(x, -y)

25. C OORDINATE RULES FOR REFLECTIONS If (a, b) is reflected in the x axis, its image is the point (, ). If (a, b) is reflected in the y axis, its image is the point (, ). If (a, b) is reflected in the y = x, its image is the point (, ). If (a, b) is reflected in the y = -x, its image is the point (, ).

26. R EFLECT THE FIGURE ACROSS THE X A XIS A ( -6, 4)B ( -1, 4) A ( -3, 10) x y

27. R EFLECT THE FIGURE ACROSS THE Y A XIS A ( -6, 4)B ( -1, 4) A ( -3, 10) x y

28. y x R EFLECT THE FIGURE GIVEN THE LINE OF IS X = 1 B (8, 4) A (3, 0) C(4, 6)

29. R EFLECT THE FIGURE GIVEN THE LINE OF IS Y = -2 y x B (8, 4) A (3, 0) C (4, 6)

30. R EFLECT THE FIGURE GIVEN THE LINE OF IS Y = 2 y x A B C D

31. R EFLECT THE FIGURE GIVEN THE LINE OF IS Y = X y x A B C D

32. R EFLECT THE FIGURE GIVEN THE LINE OF IS Y = - X AB C

33. A SSIGNMENT - P RACTICE W ORKBOOK P. 169 (1-6)

34. R OTATIONS

35. R EFRESH YOUR MEMORY - ANGLES Draw a 40 ˚ angle. Draw a 90 ˚ angle. Draw a 160˚ angle.

36. W HAT IS A ROTATION ? - A transformation in which a figure is turned about a fixed point called the center of rotation. Use the origin (0, 0) as your center of rotation (unless otherwise instructed).

37. C OORDINATE R ULES FOR ROTATIONS ABOUT THE ORIGIN W HEN A POINT ( A, B ) IS ROTATED ABOUT THE ORIGIN COUNTERCLOCKWISE, y x ( )

38. R OTATE THE FIGURE 90˚ ABOUT THE ORIGIN ( 3, 4) (5, 2) (2, 1)

39. R OTATE THE FIGURE 180˚ ABOUT THE ORIGIN ( 3, 4) (5, 2) (2, 1)

40. ( 3, 4) ( 5, 2) (2, 1) R OTATE THE FIGURE 270˚ ABOUT THE ORIGIN

41. F IND THE VALUE OF EACH VARIABLE IN THE ROTATION 105˚ y 22 15 2x + 6