Digits, Grade 8, Volume 2, Homework Helper

Topic 10: Similarity

10-1: Dilations

Key Concept

A dilation is a transformation that moves each point along the ray through the point starting from a fixed center, and multiplies distances from the center by a common scale factor.

A dilation of triangle ABC with vertices A(1, 2), B(3, 4), and C(4, 1) to triangle A´B´C´ with vertices A´(2, 4), B´(6, 8), and C´(8, 2).

If a vertex of a figure is the center of dilation, then the vertex and its image after the dilation are the same point.

A dilation of rectangle ABCD with vertices A(0, 2), B(3, 2), C(3, 0), and D(0, 0) to rectangle A´B´C´D´ with vertices A´(0, 4), B´(6, 4), C´(6, 0), and D´(0, 0). D = D´.

The scale factor is the ratio of a length in the image to the corresponding length in the original figure.

scalefactor . equals , 6 thirds , comma or 2

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Table of Contents

Digits, Grade 8, Volume 2, Homework Helper Unit D: Two-Dimensional Shapes Unit E: Measurement and Data Unit F: Personal Financial Literacy Unit G: Step-Up Lessons English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties