Reflection Objectives D Grade Reflect shapes in lines

Reflection Objectives: D Grade Reflect shapes in lines such as x = -2 or y = 1 Describe reflections fully Identify reflection symmetry in 3 -D solids C Grade Reflect shapes in lines such as y = x or y = - x Describe reflections fully 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

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

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

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

Reflection This is now applied to objects on a coordinate grid where the line of reflection is defined by an equation y-axis 10 9 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 Remember the y-axis is also the line x = 0 Remember the x-axis is also the line y = 0 x=0 8 7 6 2 squares C’ D C D’ x x 5 4 A x 3 x B’ B 3 squares 6 squares 2 36 squares A’ 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x-axis y=0

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

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

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

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

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

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