Reflection in 2-DBy: Tripti Saxena

Reflection is a transformation that produces a mirror image of an object. It is obtained by rotating the object by 180 degree about the reflection axis

InitialObject

Reflection about x

y = y

x

y

Reflection aboutorigin

x = x y = y

Reflection about y

x = x

Matrix representation of horizontal reflection

-1 0 0

0 1 0

0 0 1

1’

3’

2’

3

2

1

Original position Reflected position Reflection about the line x=0, the Y- axis , is accomplished with the transformation matrix

Matrix representation of vertical reflection

1

2 3

3’2’

1’

Original position

Reflected position

Reflection about the line y=0, the X- axis , is accomplished with the transformation matrix

1 0 0

0 -1 0

0 0 1

Example: To make a reflection about the vertical axis x = 1. Steps:

Subtract 1 from the x-coordinate. This effectively makes the x = 1 axis coincident

with the major y axis. Perform the reflection by reversing the sign of the

modified x coordinate. Add 1 to the reflected coordinate to compensate for

the original subtraction.

Example

x1 = x −1 x2 = −(x − )1 x ′ = −(x −1) +1 which simplifies to x ′ = −x + 2 y ′ = y

x ′ = −x + 2 y ′ = y or in matrix form

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