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# Graphs of Reflections

## Graph images given preimage and line of reflection

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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?

#### 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 $y-axis$to 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 $y=-x$ : $r_{y=-x}A \rightarrow Z=r_{y=-x}(x,y) \rightarrow (-y,-x)$