Dilation in Math

Dilation is a transformation that changes the size of a figure, but not its shape. When a figure is dilated, all of its points move away from or toward a fixed point called the center of dilation. The distance from the center of dilation to the pre-image is multiplied by a scale factor to obtain the image.

Understanding Dilation

When a figure is dilated, each coordinate of the original figure is multiplied by the scale factor to get the coordinates of the image. The scale factor determines how much the figure is enlarged or reduced. If the scale factor is greater than 1, the figure is enlarged; if it is between 0 and 1, the figure is reduced.

Properties of Dilation

Some important properties of dilation include:

The pre-image and image are similar.
Corresponding angles are congruent.
Corresponding sides are proportional.

Study Guide for Dilation

When studying dilation, it's important to understand the following key concepts:

Scale factor: Understand how the scale factor affects the size of the figure.
Center of dilation: Know the fixed point from which the figure is enlarged or reduced.
Similarity: Recognize that dilation produces similar figures.
Coordinates: Understand how to find the coordinates of the image after dilation.
Properties: Learn about the properties of dilation, such as congruent angles and proportional sides.

Practice drawing and dilating figures on coordinate planes, and work through problems that involve finding the image of a figure after dilation using a given scale factor and center of dilation.

Remember to also review examples and do plenty of practice exercises to strengthen your understanding of dilation.

Good luck with your studies!

◂Math Worksheets and Study Guides Seventh Grade. Algebraic Equations

The resources above cover the following skills:

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.