1. Reflections Grade 6 Copyright © Ed2Net Learning Inc.1

2. 2 Warm Up Translate the triangle up 8 units, then 6 units right. 1)

3. Copyright © Ed2Net Learning Inc.3 2) Translate the triangle left 1 unit, then 2 units down. 2. 2. Warm Up

4. Copyright © Ed2Net Learning Inc.4 3) Translate the triangle 3 units down. Warm Up

5. Copyright © Ed2Net Learning Inc.5 4) What is Translation notation? T a, b (x,y) = (x+a, y+b) 5) The original object and its translation have the same shape and size, and they face in the______ direction. same Warm Up

6. Copyright © Ed2Net Learning Inc.6 Lets review what we have learned in the last lesson Image: The new position of a point, a line, a line segment, or a figure after a transformation is called its image. Slide: Slide is a transformation in which every point of the plane figure moves in the same direction by the same distance. A slide is also called as translation. Translation: A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction.

7. Copyright © Ed2Net Learning Inc.7 Example Each vertex moves the same distance in the same direction

8. Copyright © Ed2Net Learning Inc.8 Translation Notation T a, b (x,y) = (x+a, y+b) Translation means moving the image horizontally (along the x axis) or vertically (along the y axis). Example: 7 units to the left and 3 units down. (x, y )  ( x – 7, y-3)

9. Copyright © Ed2Net Learning Inc.9 Let’s get started Flip Flip is a transformation in which a plane figure is flipped or reflected across a line, creating a mirror image of the original figure. A flip is also called a reflection.

10. Copyright © Ed2Net Learning Inc.10 Example The figure shows a flip or reflection of a parallelogram across the vertical line.

11. Copyright © Ed2Net Learning Inc.11 Reflection A reflection can be seen in water, in a mirror, in glass, or in a shiny surface. An object and its reflection have the same shape and size, but the figures face in opposite directions. In a mirror, for example, right and left are switched.

12. Copyright © Ed2Net Learning Inc.12 Example If the original object was labeled with letters, such as polygon ABCD, the image may be labeled with the same letters followed by a prime symbol, A'B'C'D'.

13. Copyright © Ed2Net Learning Inc.13 Reflecting over the x-axis When you reflect a point across the x-axis, the x coordinate remains the same, but the y-coordinate is transformed into its opposite. The reflection of the point (x, y) across the x-axis is the point (x, -y).

14. Copyright © Ed2Net Learning Inc.14 Example

15. Copyright © Ed2Net Learning Inc.15 Reflecting over the y-axis When you reflect a point across the y-axis, the y coordinate remains the same, but the x-coordinate is transformed into its opposite. The reflection of the point (x, y) across the y-axis is the point (-x, y).

16. Copyright © Ed2Net Learning Inc.16 Example

17. Copyright © Ed2Net Learning Inc.17 When you reflect a point across the line y = x, the x coordinate and the y-coordinate change places. When you reflect a point across the line y = -x, the x coordinate and the y-coordinate change places and are negated (the signs are changed). Reflecting over the line y=x or y=-x: The reflection of the point (x, y) across the line y = x is the point (y, x). The reflection of the point (x, y) across the line y = -x is the point (-y, -x).

18. Copyright © Ed2Net Learning Inc.18 Example

19. Copyright © Ed2Net Learning Inc.19 Example

20. Copyright © Ed2Net Learning Inc.20 Rules to follow when reflecting in the coordinate plane When reflecting over the line y=x: if A=(m, n), then A'=(n, m) When reflecting over the x-axis (the line y=0): if A=(m, n), then A'=(m, -n) When reflecting over the y-axis (the line x=0): if A=(m, n), then A'=(-m, n) When reflecting over the line x=a: if A=(m, n), then A'=([a- m] +a, n) When reflecting over the line y=a: if A=(m, n), then A'=(m, [a-n] +a)

21. Copyright © Ed2Net Learning Inc.21 Your Turn 1)Flip is called as a _________. Reflection 2) An object and its reflection have same ______ and size. Shape 3) The reflection of the point (x, y) across the x axis is the point _______. (x, -y) 4) The reflection of the point (x, y) across the line y= x is the point _______. ( y, x) 5) When reflection over the line y =a if A = (m,n ) then A’ = _________. [ (a-m) +a, n]

22. Copyright © Ed2Net Learning Inc.22 Your turn 6) Write the example of reflection. Water 7) The reflection of the point (x, y) across the y axis is the point _________. ( -x, y) 8) The reflection of the point (x, y) across the line y= -x is the point _______. ( -y,- x) 9)When reflection over the line x =a if A = (m,n ) then A’ = _________. [m, (a –n)+ a] 10) ______ is a transformation in which a plane is flipped. Reflection

23. Copyright © Ed2Net Learning Inc.23 1) Write the reflection about the given graph Solution: Line of reflection is half way between the two images. The line of reflection between these two triangles is y = -1.

24. Copyright © Ed2Net Learning Inc.24 2) This L-shaped figure is reflected over the y-axis. The image is then reflected over the x-axis. What are the coordinates of the vertices of the final image?

25. Copyright © Ed2Net Learning Inc.25 Solution: From the graph, identify all the points. The points are ( 2, 1 ), (4, 1), (3, 2), (3, 4), (2, 4) and (4,2). Its given the figure is reflecting over the y axis. So the points are (-2, 1), (-4, 1), (-3, 2), (-3, 4), (-2, 4) and (-4, 2). Again the figure is reflected over the x axis. So the points are (-2, -1), (-4, -1), (-3, -2), (-3, -4), (-2, -4) and (-4, -2). These are the coordinates of the final image.

26. Copyright © Ed2Net Learning Inc.26 3) In the diagram line segment TM is the line of reflection for the figure. Use this diagram to answer the following questions. a.What is the reflection image of segment AB? b.How does the length of segment EC compare to the length of segment BC? Solution: a) The reflection image of the segment AB is HC. b) EC is half of BC. In the reflection EC and BE are equal.

27. Copyright © Ed2Net Learning Inc.27 Lets review what we have learned in our lesson Flip is a transformation in which a plane figure is flipped or reflected across a line, creating a mirror image of the original figure. A flip is also called a reflection. An object and its reflection have the same shape and size, but the figures face in opposite directions.

28. Copyright © Ed2Net Learning Inc.28 The reflection of the point (x, y) across the x-axis is the point (x, -y). The reflection of the point (x, y) across the y-axis is the point (-x, y). The reflection of the point (x, y) across the line y = x is the point (y, x). The reflection of the point (x, y) across the line y = -x is the point (-y, -x).

29. GREAT JOB! Copyright © Ed2Net Learning Inc.29