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Graphs of Reflections

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Reflections: Graphs and Rules

Reflections: Graphs and Rules

Review

Transformation
A transformation is an operation that moves, ____, or changes a shape to create a new shape.
Reflection
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 \overline{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 A^\prime B^\prime C^\prime D^\prime . 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 y-axisto make the new image. Find the coordinates of the purple pentagon. On the diagram, draw and label the reflected pentagon.

Notation/Rules

We can generalize reflections by using the following template:

r_{y-axis}A \rightarrow B=r_{y-axis}(x,y) \rightarrow (-x,y)

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:

Solution:

r_{y-axis}(x,y) \rightarrow (-x,y)

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.

Solution:

a) Reflection across the y -axis: r_{y-axis}A \rightarrow B=r_{y-axis}(x,y) \rightarrow (-x,y)

b) Reflection across the x -axis: r_{x-axis}A \rightarrow O=r_{x-axis}(x,y) \rightarrow (x,-y)

c) Reflection across the y=-x : r_{y=-x}A \rightarrow Z=r_{y=-x}(x,y) \rightarrow (-y,-x)

Image Attributions

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

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