Lesson 1 Photocopy Faux Pas Develop Understanding

Learning Focus

Describe the essential features of a dilation transformation.

How do I use a dilation to enlarge or shrink a figure?

How are distance and area in a dilated image related to corresponding distances and area in the original image?

Open Up the Math: Launch, Explore, Discuss

Burnell has a new job at a copy center helping people use the photocopy machines. Burnell thinks he knows everything about making photocopies, and so he didn’t complete his assignment to read the training manual.

Mr. and Mrs. Donahue are making a scrapbook for Mr. Donahue’s grandfather’s 75th birthday party, and they want to enlarge a sketch of their grandfather which was drawn when he was in World War II. They have purchased some very expensive scrapbook paper, and they would like this image to be centered on the page. Because they are unfamiliar with the process of enlarging an image, they have come to Burnell for help.

“We would like to make a copy of this image that is twice as big, and centered in the middle of this very expensive scrapbook paper,” Mrs. Donahue says. “Can you help us with that?”

“Certainly,” says Burnell. “Glad to be of service.”

Burnell taped the original image in the middle of a white piece of paper, placed it on the glass of the photocopy machine, inserted the expensive scrapbook paper into the paper tray, and set the enlargement feature at 200%.

In a moment, this image was produced.

“You’ve ruined our expensive paper,” cried Mrs. Donahue. “Much of the image is off the paper instead of being centered.”

“And this image is more than twice as big,” Mr. Donahue complained. “One-fourth of Grandpa’s picture is taking up as much space as the original.”

A mostly blank page with Donahue's grandfather's face in the lower right corner.