Section 7.2

Rigid Motion in a PlaneReflection

Bell Work1. Describe the translation in words:2. Write the translation in arrow notation:3. Write coordinates of both polygons:

A ( , ) A’( , )⤍B ( , ) B’( , )⤍C ( , ) C’( , )⤍D ( , ) D’( , )⤍E ( , ) E’ ( , )⤍

AB

CD

E

Outcomes

• You will be able to identify what is a transformation and what is a reflection.

• You will be able to reflect a polygon on a coordinate grid across the x or y axis.

TransformationsA transformation is a change in the __size_,

_location_, or _orientation_ of a figure.

• An Isometry is a transformation that preserves length, angle measures, parallel lines, and distances between points.

• Transformations that are isometries are called Rigid Motion Transformations.

Isometry

Rigid Motion TransformationsThere are three kinds of rigid motion

transformations:

– Rotation – a “swing” around a point

– Reflection – a “flip” over a line

– Translation - a slide in one direction

Reflection

• A reflection is a transformation which flips a figure over a line .

• This line is called the line of reflection.• A Reflection is an isometry.

A’

B C C’

A

B’

Reflections

ReflectionsTheorem 7.1 Reflection Theorem – A reflection is an isometry.

Write in - All points in a reflection are moved along lines that are perpendicular to the line of reflection.

Reflections• Reflections and Line Symmetry• A figure in a plane has a line of symmetry if the

figure can be mapped onto itself by a reflection in that line.

• Different shapes have different lines of symmetry.

# of lines of symmetry?

ReflectionExample 1: ΔABC is being reflected over the x-axis. Draw and label the image ΔA’B’C’.

What are the coordinates of :

A ( , ) ⤍ A’( , ) B( , ) ⤍ B’( , )C( , ) ⤍ C’( , )

A reflection can be written as ΔABC ⤍ ΔA’B’C’A

B

C

A general rule for an x-axis reflection:(x, y) ⤍ (x, -y)

This transformation is an isometry and so the image is congruent to the original.

A’C’

B’

ReflectionExample 2: ΔABC is being reflected over the y-axis. Draw and label the image ΔA’B’C’.

What are the coordinates of :

A ( , ) ⤍ A’( , ) B( , ) ⤍ B’( , )C( , ) ⤍ C’( , )

A reflection can be written as ΔABC ⤍ ΔA’B’C’A

B

C

A general rule for a y-axis reflection:(x, y) ⤍ (-x, y)

This transformation is an isometry and so the image is congruent to the original.

ReflectionExample 3: ΔJKL which has the coordinates

J(0, 2), K(3,4), and L(5, 1).Reflect in the x-axis and then the y-axis.

Write coordinates of : J( , ) J’( , ) J’’( , ) ⟶ ⟶K( , ) K’( , ) K’’( , )⟶ ⟶L( , ) L’( , ) ⟶ ⟶ L’’( , )Describe a different combination of two reflections that would move ΔJKL to ΔJ’’K’’L’’.

Is the last image congruent to the preimage?

K’’

K

K’

Practice

Example 3: Write the rule…• When reflecting over the x-axis:

(x, y) ⤍ ( x, y)• When reflecting over the y-axis: (x, y) ⤍ ( x, y)

-

-

PracticeExample 4&5: A(0,1), B(3,4), C(5,1)

What are the coordinates of ΔA’B’C’ if reflected in line x = -1?

A ( 0, 1) ⤍ A’( , ) B( 3 , 4 ) ⤍ B’( , )C( 5 , 1) ⤍ C’( , )

What are the coordinates of A’B’C’ if reflected in line y = -2?

A( , ) ⤍ A’( , ) B( , ) ⤍ B’( , )C( , ) ⤍ C’( , )

Reflection

x = 0Or the y-axis

Reflection

y = -1

Reflection and Translation• Example 8: Quadrilateral CDEF is plotted on the grid below. • On the graph, draw the reflection of polygon CDEF over the x-axis.

Label the image C’D’E’F’.• Now create polygon C”D”E”F” by translating polygon C’D’E’F’ three

units to the left and up two units. What will be the coordinates of point C”?

C’’(-3,0)

• Don’t forget about your IP in the textbook!