1. Reflections on the Coordinate Plane

2. Reflections on the Coordinate Plane
The undisturbed surface of a pond acts like a mirror and can provide the subject for beautiful photographs

3. Reflections on the Coordinate Plane
We call the waterline a “line of symmetry” because if the photo were folded at the waterline, the two halves would form a mirror image of each other

4. Reflections on the Coordinate Plane
Similarly, the x or y-axis can act as a line of symmetry on the coordinate plane.

5. Reflections Mini-Lab
Count how many units point A is from the x-axis. Then count that many units on the opposite side of the x-axis and label this point A’ C A B
3 units
3 units A’

6. Reflections Mini-Lab
Count how many units point B is from the x-axis. Then count that many units on the opposite side of the x-axis and label this point B’ C A B
1 unit
1 unit B’ A’

7. Reflections Mini-Lab
Count how many units point C is from the x-axis. Then count that many units on the opposite side of the x-axis and label this point C’ C A B
5 units B’
5 units A’ C’

8. Reflections Mini-Lab Draw triangle A’B’C’
What do you notice about the two triangles?
Triangle A’B’C’ is a reflection of triangle ABC C A B B’ A’ C’

9. Reflections Mini-Lab
Compare the coordinates of A with A’, B with B’, and C with C’
What pattern do you notice? C A B
A (1, 3)
B (5, 1)
C (3, 5)
A’ (1, -3)
B’ (5, -1)
C’ (3, -5) B’
Same x value, Opposite y value A’ C’

10. Reflections Mini-Lab
The reflection in this mini-lab is a reflection over the x-axis.
The x-axis acts as the line of symmetry C A B
A (1, 3)
B (5, 1)
C (3, 5)
A’ (1, -3)
B’ (5, -1)
C’ (3, -5) B’ A’ C’

11. Reflections Mini-Lab
To reflect a figure over the x-axis, use the same x-coordinate and multiply the y-coordinate by -1 C A B
A (1, 3)
B (5, 1)
C (3, 5)
A’ (1, -3)
B’ (5, -1)
C’ (3, -5) B’ A’ C’

12. Reflections Mini-Lab
What do you think would happen if we multiplied the original x-coordinate by -1 and used the same y-coordinate? C’ C A B
A (1, 3)
B (5, 1)
C (3, 5)
A’ (-1, 3)
B’ (-5, 1)
C’ (-3, 5) A’ B’
You create a reflection over the y-axis!

13. Reflections Mini-Lab
What did we learn?
To reflect a figure over the x-axis, use the same x-coordinate and multiply the y-coordinate by -1
To reflect a figure over the y-axis, multiply the x-coordinate by -1 and use the same y-coordinate

14. Reflections on the Coordinate Plane Checkpoint
If square MATH is reflected into quadrant II, what is the line of symmetry?
The y-axis
M A
H T

15. Reflections on the Coordinate Plane Checkpoint
What are the coordinates of square MATH when reflected over the y-axis?
M’ (-1, 4)
M A
H T
A’ (- 4, 4)
T’ (-4, 1)
H’ (- 1, 1)

16. Reflections on the Coordinate Plane Checkpoint
If square MATH is reflected into quadrant IV, what is the line of symmetry?
The x-axis
M A
H T

17. Reflections on the Coordinate Plane Checkpoint
What are the coordinates of square MATH when reflected over the x-axis?
M’ (1,- 4)
M A
H T
A’ (4,- 4)
T’ (4,- 1)
H’ (1,- 1)

18. Homework
Practice Worksheet 11-9
Practice Skills 6-7
Due Tomorrow!!