Line of Reflections

Reflections

"I'm starting with the man in the mirror
I'm asking him to change his ways"
- Euclid of Alexandria,
OG Geometry

Graphing

Warm Up

Graph the following points:

(-6, 4) (-5, 5) (-4, 5)

(-3, 5) (-2, 4) (-5, 2)
(-3, 2)

• Reflections change the orientation and position of a figure

• The flip a shape over a line of reflection

Reflection

Reflect ΔABC over the y-axis

​There are 3 Key Questions to reflecting shapes correctly:

1. ​What is the line of reflection?

2. Where and what orientation will the new shape be?

3. What does the reflection rule actually do to the coordinates?

Line of Reflections

• The line of reflection is an imaginary line that a shape if flipped over to create a mirror image

• If you're using parchment paper to visualize the line of reflection, the line of reflection is the line that you fold the paper along

• There infinite (∞) lines of reflection, but we only focus on 4 main lines

4 Main Lines of Reflections

​X-axis

​Y-axis

​Y = -X line

​Y = X line

• ​Horizontal line that runs through zero

• ​Vertical line that runs through zero

• Increasing diagonal line that crosses zero

• Every y value equals every x value

• Decreasing diagonal line that crosses zero

• Every y value equals every negative x value

Match

Identify the line of reflection for each transformation:

x-axis

y-axis

y = x

y = -x

• x-axis

• y-axis

• y = x

• y = -x

Reflection Rules

General Rules for Reflections

Line of Reflection​	​Rule
x-axis​	( x , -y )​
y-axis​	( -x , y )​
y = x​	( y , x )​
y = -x​	( -y , -x )​

How to Interpret Reflection Rules

​Line of Reflection	Rule​	Interpretation​
​x-axis	​( x , -y )	​​​​x stays the same change the sign on y ​no swap
y-axis​	( -x , y )​	​​​​​change the sign on x y stays the same ​no swap

How to Interpret Reflection Rules

​Line of Reflection	Rule​	Interpretation​
y = x​	( y , x )​	​​x stays the same y stays the same ​x and y swap places
y = -x​	( -y , -x )​	​​​​​​change the sign on x change the sign on y ​x and y swap places

Drag and Drop

Reflect ΔABC over the y = -x line:

A ( 3 , 4 ) → A' ( -4 , ​

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)

B ( 8 , -2 ) → B' (​​

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, ​​

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)

C ( -10 , 10 ) → C' ( ​​

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, ​

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)

Drag these tiles and drop them in the correct blank above

-3

8

-2

10

-10

3

-8

2

Drag and Drop

Reflect ΔABC over the y = x line:

A ( 3 , 4 ) → A' ( 4 , ​

Placeholder

)

B ( 8 , 2 ) → B' (​​

Placeholder

, ​​

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)

C ( 10 , 10 ) → C' ( ​​

Placeholder

, ​

Placeholder

)

Drag these tiles and drop them in the correct blank above

-4

8

-2

10

-10

3

-8

2