1. Reflection Objectives: D GradeReflect shapes in lines such as x = - 2 or y = 1 Describe reflections fully Identify reflection symmetry in 3-D solids Prior knowledge: Equations of lines and how to draw them Reflect a shape in a mirror line Identify lines of symmetry in 2-D shapes Sketch 3-D shapes and draw 3-D shapes on isometric paper C GradeReflect shapes in lines such as y = x or y = - x Describe reflections fully

2. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection Identify the equations of these lines 1 1 2 3 4 5 6 7 8 2 3 4 5 6 7 8 y = x y = 7 y = 0 x = 3 x = - 8 y = x + 3 y = - x y = - x - 3

3. Reflection Reflection principles: Reflect each point of a shape separately The reflected point is the same distance from the line of reflection, the other side of the line of reflection The reflected point is plotted on a line from the object that is perpendicular to the line of reflection The original shape is the object the reflected shape is the image Line of reflection object A B C D x A’ x B’ x C’ x D’ Note that the image point has the same letter as the object point, but it has a ’ to show it is the image

4. Reflection This works for all reflection, whichever direction the line of reflection lies. Line of reflection object A B C D x A’ x B’ x C’ x D’ Note:this is not necessarily the orientation of the image that most people expect at first.

5. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection This is now applied to objects on a coordinate grid where the line of reflection is defined by an equation Reflect the object ABCD in the y-axis and label it A’B’C’D’ The squares help because all the lines are perpendicular count the squares A B C D x A’ 6 squares x 3 squares B’ C’ 2 squares x x D’ Remember the y-axis is also the line x = 0 Remember the x-axis is also the line y = 0 x = 0 y = 0

6. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection Reflect the object ABC in the line y = x and label it A’B’C’ y = x A B C A’ B’ C’

7. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection Now do these: Reflect object A in the line y = 0, label the image A’ And y = 3, label the image A’’ Reflect object B in the line y = 1, label the image B’ And y = -5, label the image B’’ A B A’A’’ B’ B’’

8. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection Now do these: Reflect object C in the line x = 0, label it C’ and x = 4, label it C’’ Reflect object D in the line x = 2, label it D’ and x = -3, label it D’’ C D C’C’’ D’

9. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection Reflect object E in the line y = x, label it E’ and y = - x, label it E’’ Reflect object F in the line y = x, label it F’ and y = - x, label it F’’ y = x E E’ F y = - x E’’ F’ F’’

10. y-axis 0 1234567 8 9 10 x-axis 10 -4 -5 -6 -7 -8 -9 -10 -3 -2 -9 -8 -7 -6 -5 -4 -3 -2 -10 1 2 3 4 5 6 7 8 9 Reflection Write the equation of the mirror line that maps A onto B A onto C B onto D F onto G A onto E B onto H C onto F G onto D C onto D D onto I DA IG B H E x = 0 C x = 4 x = - 5 F x = - 1 y =1 y =4 y =1.5 x = - 1 y =5

11. 34567 8 9 10 -9 -8 -7 -6 -5 -4 -3 -10 0 12 -2 10 1 2 3 4 5 6 7 8 9 -4 -5 -6 -7 -8 -9 -10 -3 -2 34567 8 9 10 -9 -8 -7 -6 -5 -4 -3 -10 0 12 -2 10 1 2 3 4 5 6 7 8 9 -4 -5 -6 -7 -8 -9 -10 -3 -2 34567 8 9 10 -9 -8 -7 -6 -5 -4 -3 -10 0 12 -2 10 1 2 3 4 5 6 7 8 9 -4 -5 -6 -7 -8 -9 -10 -3 -2 34567 8 9 10 -9 -8 -7 -6 -5 -4 -3 -10 0 12 -2 10 1 2 3 4 5 6 7 8 9 -4 -5 -6 -7 -8 -9 -10 -3 -2 Reflection Reflect object A in the line y = 0, label it A’ and y = 3, label it A’’ Reflect object B in the line y = 1, label it B’ and y = - 5, label it B’’ Reflect object C in the line x = 0, label it C’ and x = 4 label it C’’ Reflect object D in the line x = 2, label it D’ and x = - 3, label it D’’ C D Reflect object E in the line y = x, label it E’ and y = - x, label it E’’ Reflect object F in the line y = x, label it F’ and y = - x, label it F’’ E F Worksheet 1 Write the equation of the mirror line that maps: A onto B A onto C B onto D F onto G A onto E B onto H C onto F G onto D C onto D D onto I D A I G B H E C F A B