Page 3: Advanced Applications and Scale Factor Identification

The final page focuses on more complex applications of dilations and reverse engineering of scale factors from given coordinates.

Example: Problem 11 demonstrates how to find original coordinates when given the image coordinates and scale factor: A'(-10,-8) with k=2 leads to finding A(-5,-4).

Highlight: The page concludes with exercises requiring students to identify scale factors from given preimage and image coordinates, reinforcing understanding of the scale factor of dilation formula.

Vocabulary: Preimage - The original figure before dilation; Image - The resulting figure after dilation.

The problems on this page help students master both forward and reverse applications of dilation formulas, particularly focusing on dilations with origin at center.

Page 1: Introduction to Dilations and Scale Factors

This page introduces the fundamental concepts of dilations and their properties in geometric transformations. The content focuses on defining dilations and explaining their relationship with scale factors.

Definition: A dilation is an enlargement or reduction of a figure with respect to a fixed point, called the center of dilation.

Highlight: Dilation is not a rigid motion as it does not preserve congruency, but produces similar figures where corresponding angles remain congruent and sides are proportional.

Vocabulary: Scale factor (k) - A value that determines how much a figure will enlarge or reduce during dilation.

Example: When k > 1, the dilation results in enlargement; when k < 1, it produces a reduction.

The page includes the essential dilation formula for transformations centered at the origin: (x,y) → (kx, ky).