1. Lesson Reflections
Materials for this lesson: Piece of plain white, blue, or yellow paper
A ruler
A protractor
A pencil or pen
Your notes

2. Definition of Reflection
A reflection is a flipping of a figure over a line. This is the line of reflection. A reflection is a special type of transformation.
Line of Reflection

3. Vocabulary
-Equidistant: two points are the same distance from another point, segment or line.
-Bisector: a line segment or other figure that cuts another figure into two congruent halves.
-Perpendicular bisector: a line or segment that divides the segment into two congruent segments and is perpendicular to it. A B
l is a perpendicular bisector of AB l

4. Reflect a Figure in a Line
Draw the reflected image of quadrilateral WXYZ in line p.
Step 1 Draw segments perpendicular to line p from each point W, X, Y, and Z.
Step 2 Locate W', X', Y', and Z' so that line p is the perpendicular bisector of Points W', X', Y', and Z' are the respective images of W, X, Y, and Z.

5. Step 3 Connect vertices W', X', Y', and Z'.
Answer: Since points W', X', Y', and Z' are the images of points W, X, Y, and Z under reflection in line p, then quadrilateral W'X'Y'Z' is the reflection of quadrilateral WXYZ in line p.

6. Draw the reflected image of quadrilateral ABCD in line n.

7. Reflect a Figure in a Horizontal or Vertical Line
A. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its image over x = 1.

8. Use the horizontal grid lines to find a corresponding point for each vertex so that each vertex and its image are equidistant from the line x = 1.
Answer:

9. Reflect a Figure in a Horizontal or Vertical Line
B. Quadrilateral JKLM has vertices J(2, 3), K(3, 2), L(2, –1), and M(0, 1). Graph JKLM and its image over y = –2.

10. Use the vertical grid lines to find a corresponding point for each vertex so that each vertex and its image are equidistant from the line y = –2.
Answer:

11. p. 625

12. Reflect a Figure in the x- or y-axis
B. Graph quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3) and its reflected image in the y-axis.
Multiply the x-coordinate of each vertex by –1.
(x, y) → (–x, y)
A(1, 1) → A'(–1, 1) B(3, 2) → B'(–3, 2) C(4, –1) → C'(–4, –1) D(2, –3) → D'(–2, –3)
Answer:

13. p. 626

14. Reflect a Figure in the Line y = x
Quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection of the line y = x.
Interchange the x- and y-coordinates of each vertex.
(x, y) → (y, x)
A(1, 1) → A'(1, 1) B(3, 2) → B'(2, 3) C(4, –1) → C'(–1, 4) D(2, –3) → D'(–3, 2)
Answer:

15. p. 626

16. Homework:
Pages 81 and 82, 5-16