Page 2: Scale Factors and Their Effects

This page explores how scale factors affect dilations and the relationships between original and dilated figures.

Definition: A scale factor between 0 and 1 results in a reduction, while a scale factor greater than 1 results in an enlargement.

Example: Triangle ABC with vertices A$-2,-2$, B$-6,-2$, and C$-6,2$ is dilated by a factor of ½, producing a reduction.

Highlight: When dilating figures, all corresponding angles remain congruent while side lengths are multiplied by the scale factor.

Page 3: Determining Scale Factors

This page focuses on calculating scale factors from given coordinates and understanding transformation sequences.

Example: When point M$-3,5$ is dilated to M'$-6,10$, the scale factor can be found by comparing corresponding coordinates.

Definition: The scale factor is the ratio of the image's distance from the center to the pre-image's distance from the center.

Highlight: Complex transformations may involve both dilations and translations in sequence.

Page 4: Advanced Dilation Practice

This page provides extensive practice with various scale factors and coordinate calculations.

Example: Triangle ABC is dilated by a factor of 3, transforming A(2,1) to A'(6,3), demonstrating an enlargement.

Highlight: Scale factors can be determined by comparing corresponding coordinates of original and dilated points.

Vocabulary: Corresponding points are points that map to each other in a transformation.

Page 1: Introduction to Dilations and Transformations

This page introduces fundamental concepts of dilations and transformations through practical examples. Students learn to work with coordinate points and apply dilation rules.

Definition: A dilation is a transformation that produces a similar figure by multiplying all distances from a center point by a scale factor.

Example: Triangle DEF with vertices D$-4,1$, E(2,3), and F(2,1) is dilated by a factor of 3 using the origin, resulting in D'$-12,3$, E'(6,9), and F'(6,3).

Highlight: The rule for dilation can be written as (x,y) → (kx,ky) where k is the scale factor.

Vocabulary: Pre-image refers to the original figure, while image refers to the transformed figure.