Warm Up

1. Warm Up Tell whether the ratios form a proportion. Find the missing number.

2. Translations I can: • Define and identify translations. • Understand prime notation to describe an image after a translation. • I can describe the changes occurring to the x and y coordinates of a figure after a translation. Vocabulary: • Transformations • Translations • Congruent Figures • Parallel lines

3. Transformations change the position of a shape on a coordinate plane. *What that really means is that a shape is moving from one place to another.

4. Translation (Slide) The action of sliding a figure in any direction. *We use an arrow to represent the direction of the slide.

5. A translation does not need to be in a vertical or horizontal direction. • It can also be in a diagonal direction.

6. Translation on Lines • The size stays the same, the object is just slid to a new location. • The lines are considered parallel lines- lines are parallel if they lie in the same plane, and are the same distance apart over their entire length.

7. Translation on Angles • The angle degree stays the same, the angle is just slid to a new location.

8. Congruent Figures Figures with the same size and shape.

9. Click the Octagon to see Translation. Translation

10. Translation

11. Translation

12. Prime Notation Way to label an image after a transformation. Example: A B A’ B’ (original before transformation)(image after transformation) A’ is read as “A prime.”

13. Coordinate Plane A translation across the y-axis

14. Coordinate Plane A translation across the x-axis

15. Warm Up Tell whether the shaded figure is a translation of the non-shaded figure. If it is a translation, use an arrow to represent the direction of the slide. 1. 2. 3. 4.

16. Reflections I can: • Define and identify reflections. • Understand prime notation to describe an image after reflection. • Identify lines of reflection. • I can describe the changes occurring to the x and y coordinates of a figure after a reflection. Vocabulary: • Reflections • Line of Reflection • Line of Symmetry

17. Reflection (Flip) A transformation representing a flip of a figure over a point, line, or plane.

18. A reflection creates a mirror image of the original figure. • The original figure and its image are congruent.

19. Line of Reflection A line in which you reflect a figure over.

20. Line of Symmetry A line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side.

21. Reflection of Lines • The size stays the same, the object is just the mirror image of itself.

22. Reflection of Angles • The angle degree stays the same, the angle is just the mirror image of the original angle.

23. Horizontal flip: • Vertical flip:

24. Reflection Click on this trapezoid to see reflection. The result of a figure flipped over a line.

25. Reflection

26. Reflection

27. Reflection

28. Why is this not perfect reflection?

29. Coordinate Plane A reflection across the y-axis RULE: (x, y)  (-x, y)

30. Coordinate Plane A reflection across the x-axis RULE: (x, y)  (x, -y)

31. Warm Up Tell whether the shaded figure is a reflection of the non-shaded figure. 1. 2. 3. 4.

32. Lesson 3-3: Rotations I can: • Define and identify rotations. • Identify corresponding sides. • Understand prime notation to describe an image after a rotation. • Identify center of rotation. • Identify direction and degrees of a rotation. Vocabulary: • Rotations • Angle of Rotation • Center of Rotation

33. Rotations (Turns) A transformation in which a figure is rotated about a point called the center of rotation.

34. Angle of Rotation The number of degrees a figure rotates. 90 Degree Turn

35. Center of Rotation The point in which a figure is rotated.

36. Click the triangle to see rotation Turning a figure around a point or a vertex Rotation

37. Clockwise Rotations • 90 Degree Rotation: • 180 Degree Rotation:

38. Counter-Clockwise Rotations • 90 Degree Rotation: • 180 Degree Rotation:

39. Rotations of Lines • A line that rotates remains the same length, but will not necessarily remain parallel. Same length; rotated 90 degrees clockwiseLines are not parallel

40. Rotations of Angles • Angles that are rotated will remain the same degree measure. Same degree measure; rotated 90 degrees counter-clockwise

41. Rotation 180 Degree Clockwise Rotation

42. Lesson 3-4: Dilations I can: • I can define dilations as a reduction or enlargement of a figure. • I can identify the scale factor of the dilation. Vocabulary: • Dilations • Center of Dilation • Similar • Scale Factor • Enlargement • Reduction

43. Dilations(Shrink or Enlargement) A transformation in which a figure is made larger or smaller with respect to a fixed point called the center of dilation.

44. Center of Dilation In a dilation, it is a fixed point that a figure is enlarged or reduced with respect to it.

45. Similar The original figure and its image have the same shape but a different size.

46. Scale Factor The ratio of the side lengths of the image to the corresponding side lengths of the original figure.

47. To dilate a figure in the coordinate plane, multiply the coordinates of each vertex by a scale factor. • We will represent the scale factor with the variable k.

48. Enlargement When k>1 Examples: • Scale factor = 3 • Scale factor = 8 • Scale factor = 11

49. Reduction When 0<k<1 Examples: • Scale factor = 1/3 • Scale factor = 5/6 • Scale factor = 9/10

50. Scale Factor and Center of Dilation Here we have Igor. He is 3 feet tall and the greatest width across his body is 2 feet. He wishes he were 6 feet tall with a width of 4 feet. His center of dilation would be where the length and greatest width of his body intersect. He wishes he were larger by a scale factor of 2.