1. What type of transformation is used in inflating a balloon?

2. Types of Transformations
Reflections: These are like mirror images as seen across a line or a point with no change to the figure. (Isometry)
Translations ( or slides): This moves the figure to a new location with no change to the figure. (Isometry)
Rotations: This turns the figure clockwise or counter-clockwise but doesn’t change the figure. (Isometry)
Dilations: This reduces or enlarges the figure to a similar figure.

3. Reflections across specific lines:
To reflect a figure across the line y = a or x = a, mark the corresponding points equidistant from the line. i.e. If a point is 2 units above the line its corresponding image point must be 2 points below the line.
Example:
Reflect the fig. across the line y = 1.
(2, 3)  (2, -1).
(-3, 6)  (-3, -4)
(-6, 2)  (-6, 0)

6. Example 1
Reflect a Figure in a Horizontal or Vertical Line
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.

7. Example 1
Reflect a Figure in a Horizontal or Vertical Line
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:

8. Example 2
Reflect a Figure in the x- or y-axis
Graph quadrilateral ABCD with vertices A(1, 1), B(3, 2), C(4, –1), and D(2, –3) and its image reflected in the x-axis.

9. Example 2 Answer: Multiply the y-coordinate of each vertex by –1.
Reflect a Figure in the x- or y-axis
Answer:
Multiply the y-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)

10. Example 3
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.

11. Example 3 Answer: Interchange the x- and y-coordinates of each vertex.
Reflect a Figure in the Line y = x
Answer:
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)