1. WARM UP

2. WARM UP
1. An operation that maps a preimage onto an image is called a ___________________.
2. The preimage and the image of a transformation are ________ congruent. (Always, sometimes, or never)
3. A transformation that is an isometry _______ preserves length. (Always, sometimes, or never)

3. Review from
Yesterday

4. Isometry A transformation that preserves… Lengths Angle measures
Parallel lines
Distance between points
Transformations that are isometries are called rigid transformtions.

5. Does the transformation appear to be an isometry?

6. You can describe transformations using mappings.
What would be the “corresponding “ parts?

7. REFLECTIONS
Unit 10

8. Reflection
A transformation that uses a line like a mirror, with an image reflected in (over) a line.
The transformation is a reflection and the mirror line is the line of reflection.

9. Formally…
A reflection in a line m is a transformation that maps every point A in the plane to a point A’, so that the following properties are true:
1. If A is not on m, then m is the perpendicular bisector of 𝐴𝐴′ .

10. 2. If P is on m, then P=P’.

11. Let’s practice…
Graph the given reflection:
a. H (2,2) in the x-axis

12. G(5,4) in the line y = 4

13. c. K(3,2) in the line y = 4

14. Reflection Patterns If (x,y) is reflected in the x-axis, its image
is the point (x,-y) .

15. Reflection Patterns If (x,y) is reflected in the y-axis, its
image is the point
(-x,y) .

16. Reflection Patterns 3. Reflection in 𝑦=𝑥
Change coordinates from (x,y) to
(y,x)

17. Reflection Patterns 4. If (x,y) is reflected in 𝒚=−𝒙, its
image is the point
(-y,-x) . Swap both coordinates and negate.

18. Reflection Patterns 5. If (x,y) is reflected in the 𝒙=−𝟐, its
image is the same distance from the
line of reflection as
the pre-image.

19. Practice
P (5,4) is reflected in the x-axis. In which quadrant is its image?
P’ :
Q (5,4) is reflected in the y-axis. In what quadrant is its image?
Q’:

20. Example
Two houses (points A and B) are located on a rural road m. You want to a place cable box on the road at a point C so that the length of the cable to the box is a minimum. Where should you locate C? B A

21. Reflect A over line m to get A’. Draw 𝐴 ′ 𝐵 . B
Reflect A over line m to get A’.
Draw 𝐴 ′ 𝐵 .
This segment represents the shortest distance between A’ and B.
Why would it be the shortest distance between A and B?
Where should we put C?

22. Lines of Symmetry
A figure in the plane has a line of symmetry if the figure can be mapped onto itself by a reflection in the line.
How many lines of symmetry do you see?

23. Lines of Symmetry Can you find a hexagon that has exactly
1 line of symmetry?
2 lines of symmetry?
6 lines of symmetry?

24. Handout: 7.2 A Assignment: 7.2 B
Classwork/Homework
Handout: 7.2 A Assignment: 7.2 B