Understanding Scale Factors in Dilations

This page delves deeper into the concept of scale factors and their role in dilations:

The scale factor, denoted by k, is used to multiply coordinates or side lengths to create the new image.

Highlight: Dilations are classified based on the scale factor:

• A reduction occurs when 0 < k < 1
• An enlargement occurs when k > 1

The page includes visual examples of both reduction and enlargement to illustrate these concepts.

Example: A reduction might show a larger pre-image transformed into a smaller image, while an enlargement would show the opposite.

Dilations Inside the Coordinate Plane

This page covers coordinate plane dilation steps and examples:

To dilate a figure inside the coordinate plane, multiply each coordinate of the pre-image by the scale factor.

Example: A triangle with vertices A(-2,-2), B(1,-1), and C(0,2) is enlarged by a scale factor of 2. The resulting image has vertices A'(-4,-4), B'(2,-2), and C'(0,4).

The page includes a visual representation of this dilation on a coordinate plane, helping students understand how the transformation affects the position and size of the figure.

Key Vocabulary for Dilations

This page defines two crucial terms for understanding dilations:

Vocabulary: Dilation - A similarity transformation in which a figure is enlarged or reduced using a scale factor ≠ 0, without altering the center.

Vocabulary: Scale Factor - The number used as the multiplier when applying the dilation.

These definitions provide the foundation for understanding how dilations work and their effect on geometric figures.