1. Do Now
1) Draw a coordinate grid (like below) and label the axes 2)Graph the point (2,1) 3) Translate (2,1) 4 units up and 1 unit left 4)Write the translation algebraically

2. Review Homework
Questions?

3. Reflections
Objective: Describe reflections in the coordinate plane in algebraic terms, find new coordinates of translated polygons, and graph the reflections.

4. What is a reflection?

5. ∆ABC underwent a change and became ∆A’B’C’. Describe the change.

6. Reflection
A reflection flips a figure over a line. y x

7. (-1, 2) a) reflected over the x axis (x, y)  (___________)
New coordinates: ( )
Verbal to algebraic

8. (-1, 2) b) Reflected across the y-axis (x, y)  (___________)
New coordinates: ( )
Verbal to algebraic

9. (-1, 2) c) Reflected over the origin (x, y)  (___________)
New coordinates: ( )
Verbal to algebraic

10. (-1, 2) d) Reflected over the line y = x (x, y)  (___________)
New coordinates: ( )
Verbal to algebraic

11. (-1, 2)
e) Translated 3 units down and 1 unit left, then reflected over the line y = x
(x, y)  (___________)
New coordinates: ( )
Verbal to algebraic

12. (2, 1) a) (x, y)  (-x, y) _______________________
New coordinates: ( )
Algebraic to Verbal

13. (2, 1) b) (x, y)  (-x, -y) ______________________
New coordinates: ( )
Algebraic to Verbal

14. (2, 1) c) (x, y)  (y, x) _______________________ New coordinates: ( )
Algebraic to Verbal

15. Special Reflections Reflection across x – axis:
Reflection across y – axis:
Reflection over origin:
Reflection over line y = x:
(x, y )  (x, -y)
(x, y )  (-x, y)
(x, y )  (-x, -y)
(x, y )  (y, x)

16. Right 2 units, down 3 units, AND reflected in the Y-AXIS
REFLECTIONS
X-AXIS
ORIGIN
Y=X
Right 2 units, down 3 units, AND reflected in the Y-AXIS
Triangle
A(6, 4)
B(2, 7)
C(8, 12)
( x, y)  ( )
New Points:
( , )
(x, y)  ( )
(x, y)  ( )

17. 1. A’B’C’ is the image produced after reflecting ABC over the line y = x. If vertex B has coordinates (s, t), what are the coordinates of B’ ?
A (s, -t)
B (t, s)
C (-s, t)
D (-s, -t)

18. What is the rule for the transformation formed by a translation one unit to the left and two units up followed by a reflection over the y-axis?
A (x – 1, y + 2)
B [-(x – 1), y + 2]
C [-(x – 1), -(y – 4)]
D [x – 4, -(y – 1)]

19. Point R(a, b) is a vertex of quadrilateral QRST
Point R(a, b) is a vertex of quadrilateral QRST. What are the coordinates of R after QRST is reflected over the x-axis? A (b, a) B (-a, b) C (-a, -b) D (a, -b)

20. The point A(-1, 3) is transformed according to the rule (x’y’) = (x – 2, y + 1). The image of A’ is then reflected over the origin, resulting in point A’’. What are the coordinates of A’’? A (-3, 4) B (3, -4) C (4, -3) D (-3, -4)

21. Homework
Reflections Worksheet