Transformations – Translations and Reflections

1. Transformations –Translations and Reflections HW #1

2. Defining a Transformation A transformation is an operation that maps, or moves, a figure onto an image.

3. What is a RIGID or ISOMETRIC transformation? A rigid/isometric transformation does not alter the size or shape of the original object. How can you move an object without changing its size or shape?

4. Defining a Translation A translation is a “slide” of an object on the coordinate plane. It can be described using words: Up, Down, Left, Right

5. Example 1 Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure. a. b. c. SOLUTION No, this is not a translation. The image is a mirror image of the original figure. a. b. c. No, this is not a translation. The original figure is rotated. Yes, this is a translation.

6. Defining a Translation A translation can be described as a function using coordinates: ( x , y )  ( x + a , y + b) The amount of up/down movement The amount of left/right movement

7. Defining a Translation Using this notation, which part describes the input and the output? ( x , y )  ( x + a , y + b) Example: Given the point ( -9 , 2 ), where would the image point be given the following translation? ( x , y )  ( x - 5 , y +8)

8. Example 2 Describe the translation of the segment. SOLUTION Point P is moved 4 units to the right and 2 units down to get to point P'. So, every point on PQ moves 4 units to the right and 2 units down. Describe Translations *Notice the notation to differentiate between the original points, and the image points!*

9. Example 3 The translation can be described using the notation (x, y)(x – 3, y + 4). ANSWER Use Coordinate Notation Describe the translation using coordinate notation. Did the triangle change shape or size?

10. Checkpoint ANSWER Each point is moved 3 unitsto the left and 4 units down;(x,y) (x – 3,y – 4). ANSWER Each point is moved 5 units to the left and 2 units up; (x,y)(x – 5,y + 2). Describe Translations Describe the translation using words and coordinate notation. 4. 5.

11. Checkpoint Draw Translated Figures Draw the image of the figure after the given translation. Make sure to label the image properly! a. (x,y)(x + 3,y – 2) ANSWER (x,y)(x – 3,y + 4) b. ANSWER The amount of left/right movement

12. Defining a Reflection A reflection is an isometrictransformation that creates a mirror image. The original figure is reflected over a line that is called the line of reflection.

13. Checkpoint Identify Reflections Tell whether the red figure is a reflection of the blue figure. If the red figure is a reflection, name the line of reflection. 1. 3. 2. ANSWER ANSWER ANSWER yes; the x-axis yes; the y-axis no

14. Line of Reflectional Symmetry If a figure can be reflected onto itself, then it has a line of reflectional symmetry.

15. Example 4 Determine Lines of Symmetry Determine the number of lines of symmetry in a square. SOLUTION Think about how many different ways you can fold a square so that the edges of the figure match up perfectly. vertical fold horizontal fold diagonal fold diagonal fold A square has four lines of symmetry. ANSWER

16. Example 5 Determine Lines of Symmetry Determine the number of lines of symmetry in each figure. c. b. a. SOLUTION a. 2 lines of symmetry c. 6 lines of symmetry b. no lines of symmetry

17. Checkpoint Determine Lines of Symmetry Determine the number of lines of symmetry in the figure. 1. 1 ANSWER 2. 2 ANSWER 3. 4 ANSWER