1. Reflections or Flips

2. Objectives Draw reflected images Across x-axis Across y-axis
Across line y = x

3. Equal Distance from Reflection Line
Reflections y x
Across the x-axis
Multiply y coordinate by -1 y x
Across the y-axis
Multiply x coordinate by -1 A A’ A B B’ B C C’ C B’
KEY:
Equal Distance from Reflection Line C’ A’ y x
Across the line y = x
Interchange x and y coordinates B A B’ C C’ A’

4. Common reflections in the coordinate plane
x-axis
y-axis
y = x
Pre-image to image
(a, b)  (a, -b)
(a, b)  (-a, b)
(a, b)  (b, a)
Find coordinates
Multiply y coordinate by -1
Multiply x coordinate by -1
Interchange x and y coordinates
A line of symmetry is like a line of reflection.
The line of symmetry in a figure is a line where the figure could be folded in half so that the two halves match exactly

5. 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.
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.
Step 3 Connect vertices W', X', Y', and Z'.
Example 1-1a

6. Draw the reflected image of quadrilateral ABCD in line n.
Answer:
Example 1-1b

7. COORDINATE GEOMETRY Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the x-axis. Compare the coordinates of each vertex with the coordinates of its image.
Use the vertical grid lines to find the corresponding point for each vertex so that the x-axis is equidistant from each vertex and its image. D'
A(1, 1)  A' (1, –1) C'
B(3, 2)  B' (3, –2)
C(4, –1)  C' (4, 1) A' B'
D(2, –3)  D' (2, 3)
Answer: The x-coordinates stay the same, but the y-coordinates are opposite. That is, (a, b)  (a, –b).
Example 1-2a

8. COORDINATE GEOMETRY Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3). Graph ABCD and its image under reflection in the y-axis. Compare the coordinates of each vertex with the coordinates of its image.
Use the horizontal grid lines to find the corresponding point for each vertex so that the y-axis is equidistant from each vertex and its image. B'
A(1, 1)  A' (–1, 1) A'
B(3, 2)  B' (–3, 2)
C(4, –1)  C' (–4, –1) C'
D(2, –3)  D' (–2, –3) D'
Answer: The x-coordinates are opposite, but the y-coordinates stay the same. That is, (a, b)  (–a, b).
Example 1-3a

9. COORDINATE GEOMETRY Suppose quadrilateral ABCD with A(1, 2), B(3, 5), C(4, –3), and D(2, –5) is reflected in the line y = x. Graph ABCD and its image under reflection in the line y = x. Compare the coordinates of each vertex with the coordinates of its image.
The slope of y = x is 1. AA’ is perpendicular to y = x so its slope is –1. From A to the line y = x move down ½ unit and right ½ unit. From the line y = x move down ½ unit, right ½ unit to A'. C'
A(1, 2)  A'(2, 1) B'
B(3, 5)  B'(5, 3) D'
C(4, –3)  C'(–3, 4) A'
D(2, –5)  D'(–5, 2)
Plot the reflected vertices and connect to form the image A'B'C'D'.
Answer: The x-coordinate becomes the y-coordinate and the y-coordinate becomes the x-coordinate. That is, (a, b)  (b, a).
Example 1-5a

10. Summary & Homework Summary: Homework:
Line of Symmetry – a line across which the figure could be folded in half
Point of Symmetry – even numbered regular figures only for us
Homework:
pg ; , 28-30, 35-36, 44-47
Reflection
x-axis
y-axis
origin
y = x
Pre-image to image
(a, b)  (a, -b)
(a, b)  (-a, b)
(a, b)  (-a, -b)
(a, b)  (b, a)
Find coordinates
Multiply y coordinate by -1
Multiply x coordinate by -1
Multiply both coordinates by -1
Interchange x and y coordinates