1. Rigid Motion in a Plane Reflection
Section 7.2
Rigid Motion in a Plane
Reflection

2. Bell Work A B C D E Describe the translation in words:
Write the translation in arrow notation:
Write coordinates of both polygons:
A ( , ) ⤍ A’( , )
B ( , ) ⤍ B’( , )
C ( , ) ⤍ C’( , )
D ( , ) ⤍ D’( , )
E ( , ) ⤍ E’ ( , )

3. 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.

4. Transformations Isometry
A transformation is a change in the __size_, _location_, or _orientation_ of a figure.
Isometry
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.

5. Rigid Motion Transformations
There 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

6. 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’ A B C C’ B’

7. Reflections

8. Reflections
Theorem 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.

9. 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?

10. Reflection
Example 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 general rule for an x-axis reflection:
(x, y) ⤍ (x, -y) A’ C’ B’
This transformation is an isometry and so the image is congruent to the original. B
A reflection can be
written as
ΔABC ⤍ ΔA’B’C’ C A

11. Reflection
Example 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 general rule for a y-axis reflection:
(x, y) ⤍ (-x, y) B
This transformation is an isometry and so the image is congruent to the original.
A reflection can be
written as
ΔABC ⤍ ΔA’B’C’ C A

12. Reflection
Example 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’’( , ) K
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’

13. Practice Example 3: Write the rule… When reflecting over the x-axis:
(x, y) ⤍ ( x, y)
When reflecting over the y-axis: - -

14. Practice Example 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’( , )

15. Reflection
x = 0
Or the y-axis

16. Reflection
y = -1

17. 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)

18. Don’t forget about your IP in the textbook!