1. What do you see when you look in a mirror?
Reflections
What do you see when you look in a mirror?

2. Reflections
A reflections flips an image across a line, called the Line of Reflection
In a reflection the orientation changes but the size remains the same.

3. Reflecting Across Line l
A reflection across line l is a transformation with the following properties:
If point P is on line l then P’ = P
If point P is not on l, then line l is the perpendicular bisector of segment
The notation for the reflection is Rl P where P is the object being reflected

4. Reflecting Across Any Line (Honors Only)
Procedure to find R l P for point P and line l
Find l’ so that l’  l and P is on l’
Find the intersection of l and l’ . This is also the midpoint M of
Find P’ using the midpoint formula or point stacking method

5. Reflecting Across Any Line (Honors Only)
Example: Find P’ = R y=2x+3 (4,1)
1. Find l’ : The original slope is 2;
So, the perpendicular slope = -1/2
By point-slope: y – 1 = -1/2(x - 4) => y = -1/2x + 3
2. Find M: the intersection of l and l’
2x + 3 = -1/2x + 3
Solve to get x = 0,
Use x = 0 to get y = 3.
So, M = (0, 3)
3. Find P’: P = ( 4, 1 )
M = ( 0, 3 )
So, P’ = ( -4, 5 ) l P’ l' P

6. Reflection Shortcuts x – axis: Keep x, change y. (X,Y)  ( X, -Y )
y – axis: Keep y, change x. (X,Y)  (-X, Y )
y = x: Swap x and y. (X,Y)  ( Y, X )
y = -x: Swap x and y & change sign
(X,Y)  (-Y, -X )

7. Reflecting over the x and y-axis
Example 1: Find R x-axis (2,1)
Rule: keep x, change y
Example 2: Find R y-axis (2,3)
Rule: keep y, change x A A’
R x-axis (2,1)  (2, -1) A’ A
R y-axis (2,3)  (-2, 3)

8. Reflecting over y = x or y = -x
Example 3: Find R y = x (4,2)
Rule: swap x and y
Example 4: Find R y = -x (2,3)
Rule: swap x and y,
change signs A A’
R y = x (4,2)  (2, 4) A’ A
R y = -x (2,3)  (-3, -2)

9. Reflecting Polygons Reflect each of the vertices
Example 5: Graph R x-axis ABC, given A(1, 2), B(1, 4) and C(4, 4) Rule: Keep x change y A(1, 2)  A’(1, -2), B(1, 4)  B’(1, -4) and C(4, 4)  C’(4, -4) B C A A’ B’ C’

10. Corresponding Parts Corresponding parts of reflected polygons are congruent to the original
Example 6: Find A’C’ given AC = 2x+4 and A’C’ = 3x - 2 Corresponding parts are congruent So, AC = A’C’ or 2x + 4 = 3x -2 Solving for x, x = 6 A’C’ = 3x -2 = 3(6) – 2 = 16 B C A A’ B’ C’

11. Summary Thank you! Defined a reflection and line of reflection
Reflected a point across a line
Shortcuts for Reflection
Reflected a polygon across a line
Corresponding parts of reflected polygons
Thank you!