What type of transformation is used in inflating a balloon?

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What type of transformation is used in inflating a balloon?

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.

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)

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.

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:

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.

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)

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.

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)