### 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 -axis: values are multiplied by ___.
- reflections across the -axis: __ values are multiplied by -1.
- reflections across the line : and values
places**switch** - reflections across the line . and values switch places and are multiplied by __.

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

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#### Practice Questions:

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

2) he diamond is reflected across the line to form the image . 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 .

4) The purple pentagon is reflected across the 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:

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:

2) Reflect Image A in the diagram below:

a) Across the -axis and label it .

b) Across the -axis and label it .

c) Across the line and label it .

Write notation for each to indicate the type of reflection.

Solution:

a) Reflection across the -axis:

b) Reflection across the -axis:

c) Reflection across the :