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.

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.

This page explains how to perform dilations of two-dimensional figures when they are not on a coordinate plane:

To dilate an object outside the coordinate plane, multiply each side length by the scale factor.

Example: A triangle with side lengths 6 in, 8 in, and 10 in is reduced by a scale factor of 1/2 $k = 0.5$. The resulting image has side lengths of 3 in, 4 in, and 5 in.

Highlight: To verify the scale factor, the ratio of each image side to its corresponding pre-image side should remain constant.

This method allows for precise dilations of figures without relying on a coordinate system.

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.

This page focuses on calculating scale factor for dilation in geometry when given two similar figures:

To find the scale factor between two figures, use the ratio of corresponding sides from the image and pre-image.

Example: Given two similar triangles with corresponding sides of 8 and 12 units, the scale factor can be calculated as 8/12, which simplifies to 2/3.

This method allows students to determine the scale factor used in a dilation by comparing the dimensions of the original and transformed figures.

The final page encourages further practice and understanding:

It directs students to watch a video within the lesson for more examples of dilations.

Highlight: The page includes a visual example of a dilation with a scale factor of 3 on a coordinate plane, reinforcing the concepts learned throughout the guide.

This concluding section emphasizes the importance of practice and provides resources for students to deepen their understanding of dilations in geometry.

This page introduces the topic of dilations as a type of geometric transformation applied to two-dimensional figures. Dilations are an essential concept in geometry that allows for the scaling of shapes while preserving their proportions.