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Graphs of Reflections

Graph images given preimage and line of reflection

Atoms Practice
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Reflections: Graphs and Rules

Reflections: Graphs and Rules


A transformation is an operation that moves, ____, or changes a shape to create a new shape.
A reflection is an example of a transformation that flips _____ of a shape over the same line.
Line of Reflection
The line of reflection is the line that a shape _____ (flips) across when undergoing a reflection.

Each point on the preimage will be the same distance from the line of reflection as it's corresponding point in the image.

  • reflections across the x -axis: y values are multiplied by ___.
  • reflections across the y -axis: __ values are multiplied by -1.
  • reflections across the line y=x : x and y values switch places
  • reflections across the line y=x . x and y values switch places and are multiplied by __.

What is the reflection across the line y=x called?

License: CC BY-NC 3.0

Click here for answers.

Practice Questions:

1) Line AB¯¯¯¯¯¯¯¯ drawn from (-5, 3) to (7, 3) has been reflected across the x -axis. Draw the preimage and image and properly label each.

2) he diamond ABCD is reflected across the line y=x to form the image ABCD. Find the coordinates of the reflected image. On the diagram, draw and label the reflected image.

3) Draw a triangle with vertices at points (-2, 3), (-3,1) and (1,1).  Then reflect the triangle across the line y=x.

4) The purple pentagon is reflected across the yaxisto make the new image. Find the coordinates of the purple pentagon. On the diagram, draw and label the reflected pentagon.


We can generalize reflections by using the following template:


Reflection notation helps us describe the movement of a figure more generally, generalizing the coordinates from (2,3) for example, to (x,y). 

1) Describe the following reflection using reflection notation:



2) Reflect Image A in the diagram below:

a) Across the y -axis and label it B .

b) Across the x -axis and label it O .

c) Across the line y=x and label it Z .

Write notation for each to indicate the type of reflection.


a) Reflection across the y -axis: ryaxisAB=ryaxis(x,y)(x,y)

b) Reflection across the x -axis: rxaxisAO=rxaxis(x,y)(x,y)

c) Reflection across the y=x : ry=xAZ=ry=x(x,y)(y,x)

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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