ReflectionsReflections Day 119Day 119

Learning Target:Students can represent transformations in the plane; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

Reflections…

A A rereflflectionection “ “flflips” an object ips” an object and can be seen in water, in a and can be seen in water, in a mirror, in glass, or in a shiny mirror, in glass, or in a shiny surface.  An object and its surface.  An object and its reflection have the reflection have the same same shape and sizeshape and size, but the , but the figures face in opposite figures face in opposite directionsdirections.  In a mirror, for .  In a mirror, for example, right and left are example, right and left are switched. switched.

The line (where a mirror may be placed) is The line (where a mirror may be placed) is called the called the line of reflectionline of reflection.  The distance .  The distance from a point to the line of reflection is the same from a point to the line of reflection is the same as the distance from the point's image to the as the distance from the point's image to the line of reflection. A reflection can be thought of line of reflection. A reflection can be thought of as a "flipping" of an object over the line of as a "flipping" of an object over the line of reflection. reflection.

The object ABCD is being reflected over the x-axis.

Reflect across the x-Reflect across the x-axisaxis

x,y x, y Change the sign of the y-value

Reflect across the x-Reflect across the x-axisaxis

C 2,4

A 0, 8

T 3,5

C ' 2, 4

A' 0,8

T' 3, 5

Reflect across the Reflect across the y-axisy-axis

x,y x,y Change the sign of the x-value

Reflect across the Reflect across the y-axisy-axis

H 1,2

A 3, 5

T 4, 1

H' 1,2

A' 3, 5

T' 4, 1

Reflect across y Reflect across y = x= x

x,y y,xSwap x and y

Reflect across y Reflect across y = x= x

B 7, 12 B' 12, 7

A' 2,8

T' 13,9

A 8, 2

T 9,13

Reflect across y Reflect across y = -x= -x

x,y y, x Swap and change both signs

Reflect across y Reflect across y = -x= -x

W 13,21 W' 21, 13

E' 9,2

B' 24, 17

E 2,9

B 17, 24

Classwork…Classwork…

Reflections by Hand

& Reflections Using a

Mira