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

Labelling

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

Drag labels to their correct position on the image

Image

Pre-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

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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