1. 4.2 Reflections
Warm Up Maintaining Mathematical Proficiency:  Find the measure of each variable.  Justify your solution.

2. 4.2 Reflections

3. 4.2 Reflections
Learning Check:

4. 4.2 Reflections
Reflection - A transformation or Rigid Motion that uses a line like a mirror to reflect a figure.
Reflections across Vertical and Horizontal Lines: Graph triangle ABC with vertices at A(1, 3), B(5, 2), and C(2, 1) and its image after the reflection described.
                 1) x = -1                                            2) y = 3 

5. Learning Check: Reflections with Vertical and Horizontal Lines.
Graph triangle ABC with vertices at A(1, 3), B(5, 2), and C(2, 1) and its image after the reflection described.
         
          3) line n: x = 3                                            4) line m: y = 1 

6. 4.2 Reflections
Reflection Across y = x

7. Bellwork: Find the measure of each variable. Justify your answer.
4.2 Reflections
Bellwork: Find the measure of each variable. Justify your answer.

8. Reflection Across y = -x
4.2 Reflections
Reflection Across y = -x
Graph the triangle and its image after the reflection across line y = -x.
Procedure:
1) Plot the points and graph the Line of Reflection.
2) Find the slope of a line perpendicular to the Line of Reflection.
3) Using a line segment perpendicular to the Line of Reflection, reflect each point.  The Line of Reflection will be half way between the Initial Point and the Terminal Point. 

9. Learning Check: Reflection Across y = x
4.2 Reflections
Learning Check: Reflection Across y = x
Graph the quadrilateral and its image after the reflection across line y = x.
Procedure:
1) Plot the points and graph the Line of Reflection.
2) Find the slope of a line perpendicular to the Line of Reflection.
3) Using a line segment perpendicular to the Line of Reflection, reflect each point.  The Line of Reflection will be half way between the Initial Point and the Terminal Point. 

10. 4.2 Reflections
Mathematical Connections: The line y = 3x + 2 is reflected across the line y = -1.  What is the equation of its image?

11. 4.2 Reflections
Mathematical Connections: Point B'(1, 4) is the image of B(3, 2) after a reflection across line c.  Without graphing, find a possible equation of line c.

12. 4.2 Reflections
Learning Check: Point A'(-4, 0) is the image of A(-2, 2) after a reflection across line c.  Without graphing, find a possible equation of line c.
Information you may need.
1) Slope of a Line. 
2) Perpendicular lines have negative reciprical slopes.
3) Midpoint.
4) Slope-Intercept Equation of a Line.

13. 4.2 Reflections 1) -(-x) x 2) -(x + 3) -x - 3 3) x - (12 – 5x) 6x - 12
 Maintaining Mathematical Proficiency:  Simplify each expression. 
1)  -(-x)
             x
2)  -(x + 3)
          -x - 3
3)  x - (12 – 5x) 
         6x - 12
4)   x - (-2x + 4)
          3x - 4