# Transformations: Reflection

### By: Yosep Rhe & Helen Yoo

## Definition

A type of transformation that reflects,or "flips", a graph or figure across a line,called the line of reflection. A reflection is a type of isometry. An isometry (aka congruence transformation or rigid motions) is a transformation that doesn't change the shape or size of a figure.

## Rules of Reflection

Reflect over...

X-axis: (x,y) -> (x,-y)

Y-axis: (x,y) -> (-x,y)

Y=X: (x,y) -> (y,x)

## Reflection over x-axis (Click on the image to see the image for all...) Rule: (x,y) -> (x,-y) Coordinates: A: (-2,1) -> (-2,-1) B: (2,4) -> (2,-4) C: (4,2) -> (4,-2) | ## Reflection over y-axis Rule: (x,y) -> (-x,y) Coordinates: A: (2,2) -> (-2,2) B: (4,4) -> (-4,4) C: (5,1) -> (-5,1) | ## Reflection over y=x Rule: (x,y) -> (y,x) Coordinates: A: (-4,2) -> (2,-4) B: (-3,-1) -> (-1,-3) C: (-5,-2) -> (-2,-5) |

## Reflection over x-axis (Click on the image to see the image for all...)

Rule: (x,y) -> (x,-y)

Coordinates:

A: (-2,1) -> (-2,-1)

B: (2,4) -> (2,-4)

C: (4,2) -> (4,-2)

## Reflection over y-axis

Rule: (x,y) -> (-x,y)

Coordinates:

A: (2,2) -> (-2,2)

B: (4,4) -> (-4,4)

C: (5,1) -> (-5,1)