Dilations – part 1 Objective: When done with this lesson, you will have investigated scale factor and center of dilation the effect a dilation has on lengths and areas Washington State GLE: Approximate completion time: 3 hours

Photographs, drawings, and images often go through some transformation to change size. Some changes are called distortions while others are called dilations. Fun house mirrors cause amusing distortions. You hope the picture on your driver's license is a dilation—unless you'd rather have a fun distortion for your photo ID.

Click on the herring in this picture of the penguins to watch dilations and distortions.
Can you guess which is a distortion and which is a dilation?

To grasp what happens in a dilation, you will be diving into a few investigations. Grab your pencil, graph paper, straight edge, and inquisitive attitude for these investigations.

Please open up a word document to keep your notes for each of the investigations.
Be sure to keep good notes and title each investigation section.

Investigation 1.

In this investigation you will be play with a virtual manipulative to investigate "scale factor" and "center of dilation".

When you're ready to go, click here to open a new window for investigation 1.

 

Investigation 2.

In this investigation you will be considering the transformation defined by
this rule: P(x, y) → P'(x, 3y). Is it a true dilation or is it a distortion?

When you're ready to go, click here to open a new window for investigation 1.

Investigation 3.

In this investigation you will be considering the size transformation of magnitude 3 defined by
this rule: P(x, y) → P'(3x, 3y). You will look carefully at what happens to lengths and areas in this investigation.

When you're ready to go, click here to open a new window for investigation 1.