Reflections

Section 9-1

Reflection

A reflection is a transformation representing a flip of a figure

To abbreviate reflection in line j, we write Rj.

To abbreviate Rj maps P to P’, we write .PPR j :

A reflection in a line is an isometry ( a congruence transformation).

Since a reflection is an isometry, it preserves distance and angle measure.

It is also possible to reflect an image with respect to a point.

Point P is the reflection of R with respect to Q. Therefore, Q is a point of reflection.

P Q R

Lines and Points of Symmetry

Some figures can be folded so that the 2 halves match. The fold is a line of symmetry.

For some figures, a point can be found that is a common point of reflection for all points on a figure. This point is called a point of symmetry.

4 lines of symmetry

Point of symmetry

1 line of symmetry

No point of symmetry

ReflectionsReflection x-axis y-axis origin y=x

Preimage to Image

How to find coordinates

Multiply the y-coordinate by -1

Multiply the x-coordinate by -1

Multiply both coordinates by -1

Interchange the x and y coordinates

( , ) ( , )a b a b

( , ) ( , )a b a b

( , ) ( , )a b b a

( , ) ( , )a b a b

Joke Time

Why did the tomato blush?

He saw the salad dressing!

What did the dog yell when it saw the pieces of a fallen tree?

Bark! Bark!