Dilation

Dilation is a transformation that changes the size of a figure but not its shape. When a figure is dilated, it becomes larger or smaller, depending on the scale factor used. The scale factor determines how much larger or smaller the figure becomes. Here's how dilation works:

Scale Factor

The scale factor, denoted by the letter "k", is the ratio of the length of a side of the image to the corresponding side of the pre-image. If the scale factor is greater than 1, the image is an enlargement; if the scale factor is between 0 and 1, the image is a reduction.

Dilation of a Point

When a point is dilated about a center, the distance between the center and the point is multiplied by the scale factor to find the coordinates of the dilated point. If the scale factor is greater than 1, the point moves farther away from the center; if the scale factor is between 0 and 1, the point moves closer to the center.

Dilation of a Line Segment

To dilate a line segment, you multiply the length of the segment by the scale factor to find the length of the dilated segment. The orientation of the line segment remains the same, but its length changes according to the scale factor.

Dilation of a Polygon

When dilating a polygon, each vertex of the polygon is dilated about a center to form the corresponding vertices of the dilated polygon. The sides of the polygon are also dilated according to the scale factor.

Study Guide

Here are some key points to remember when studying dilation:

Understand the concept of scale factor and how it affects the size of a figure during dilation.
Practice dilating points, line segments, and polygons using different scale factors.
Remember that dilation does not change the shape of a figure, only its size.
Be familiar with the coordinates of the original figure and how they change when dilated.
Work on problems involving both enlargement and reduction to grasp the full concept of dilation.

With a good understanding of dilation, you'll be able to manipulate and transform figures in a way that preserves their shape while changing their size.

◂Math Worksheets and Study Guides Sixth Grade. Tables

The resources above cover the following skills:

Data Analysis and Probability (NCTM)

Select and use appropriate statistical methods to analyze data.

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.