T2.L3. Reflections as Functions

L E A R N I N G O B J E C T I V E :
S W B A T P R O V E E Q U I D I S T A N C E B E T W E E N T H E E N D PO I N T S O F A S E G M E N T A N D P O I N T S O N I T
P E R P E N D I C U L A R B I S E C T O R U S I N G T H E
P R O P E R T I E S O F R E F L E C T I O N .

Reflection As
Functions

Vocabulary!

• Reflection Function: A reflection as a function, Rℓ, takes as its input, P, the location of a point with respect to some line of reflection ℓ and outputs Rℓ (P), or the opposite of the location of P with
respect to the line of reflection.

•Perpendicular Bisector Theorem: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.

• Proof: A proof is a series of statements and corresponding reasons forming a valid argument that starts with a hypothesis and arrives at a conclusion.

Line of Reflection

Let's Investigate the figure below:

1. What do we notice about A and A' as it relates

to the line of reflection?

2. Which image is your pre-image?

3. Write Congruence and Equality statements about the two images.

Categorize

Options (6)

$$\overline{AB\ }=\overline{A'B'}$$  

$$\overline{BC}=\overline{B'C'}$$  

$$\overline{AC\ }=\overline{A'C'}$$  

$$\overline{AB}\cong\overline{A'B'}$$  

$$\overline{BC}\cong\overline{B'C'}$$  

$$\overline{AC}\cong\overline{A'C'}$$  

Organize the following statements for the given image.

Equality Statement

Congruency Statement

Labeling

Lable the pre-image and image of the given figure.

Drag labels to their correct position on the image

Pre-image

Image

Multiple Choice

True or False:

Corresponding vertices are equidistant from the line of reflection?

• True

• False

Reflection Functions

•Let's write a function for the reflection of the trapezoid.

How does the function represent the reflection of the trapezoid?

Fill in the Blanks

Give me the reflection function for the given pre-image and image.

Perpendicular Bisector Theorem

What do you notice about the relationship between point P and points R and B?

Prove: Line PB = Line PR

Why does Line PB = Line PR?

Reorder

Put the proof for the given figure in the right order.

Prove: Line segment PB = Line segment PR

• The reflection of point "P" on line "L" is point "P"

• Because line "L" is the perpendicular bisector of line segment RB, the reflection of point "R" across line "L" is point "B".

• The reflection of line segment PR across line "L" is line segment PB

• Therefore Line segment PR =Line segment PB

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