Question

What is the rule for the reflection?

Answer 1

Reflection in the line y = x. A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A'. The general rule for a reflection in the y-axis: (A, B) (B, A)

Answer 2

A reflection is an example of a transformation that takes a shape (called the pre-image) and flips it across a line (called the line of reflection) to create a new shape (called the image).

The most common lines of reflection are the x-axis, the y-axis, or the lines y=x or y=−x.

The x-axis,

Reflection across the x-axis:
`T_(x-axis)` (3,2)→(3,−2)

i.e. for reflection across the x-axis the x-coordinate remains same and y-coordinate change to negative sign.

The y-axis

Reflection across the y-axis:
`T_(y-axis)` (3,2)→(-3,2)

i.e. for reflection across the y-axis the y-coordinate remains same and x-coordinate change to negative sign.

The line y=x

Reflection across the line y=x:
`T_(y=x)` (3,2)→(2,3)

For reflection across y=x the x and y value get interchanged.

The line y=−x.

Reflection across the line y=−x:
`T_(y=-x)` (3,2)→(−2,−3)

For reflection across y=-x the x and y value get interchanged with opposite signs.