Question

How are reflections represented as a function? what is the relationship between a reflection and a rigid motion?

Answer 1

Reflections are a type of transformation that move an entire curve such that its mirror image lies on the other side of the x or y axis.

A vertical reflection is given by the equation y=−f(x) and results in the curve being "reflected" across the x-axis. A horizontal reflection is given by the equation y=f(−x) and results in the curve being "reflected" across the y-axis.

Reflection is one of the four basic rigid motions.

Four basic rigid motions: 

1.Reflection 

2.Glide Reflection 

3.Rotation 

4.Translation

Answer 2

Answer with explanation:

→→→Reflection is done through a line.When you reflect an Object through a line the Pre-image before reflection and Image Obtained after reflection are congruent to one another.

Reflection is done through a line.

The equation of line can be

1. x=k

2. y=k

3.x +y=k

where, k is any real number.

→→→When you talk about rigid motion , then there are four kind of transformation that can take place in the object called Pre-Image which are

1.Translation

2.Dilation

3. Rotation

4. Reflection

Apart from dilation , in all other cases Pre-image and Image are congruent while in all cases the two are similar.