A dilation is a reduction or an enlargement of an object. If the scale factor is less than 1, then the dilation is a reduction. If the scale factor is greater than 1, then the dilation is an enlargement.

An example of using an enlargement is when a builder constructs a house using a blueprint.

Architects and builders use dilations and similar figures to obtain the correct measurements to create structures.

A builder uses a scale factor greater than 1 to create an enlargement when constructing a house. If an architect were creating the blueprint of a house that has already been built, she would use a dilation. However, the dilation would be a reduction since it would have a scale factor of less than 1.

The measurements on the blueprint are the dimensions of actual rooms. In each case, the width is the first number, and the length is the second number. (width x length)

Given:
width of blueprint bedroom over width of actual bedroom width of blueprint bedroom width of actual bedroom = 0.25 ft over 8 ft 0.25 ft 8 ft

(Note: the dimensions are in feet!)

Use the floor plan and your knowledge of ratios and proportions to drag the correct answer to the correct blank. Use your finished results to answer the questions that follow.

• If the scale factor from the actual room to the blueprint is 1 over 32 1 32 , what would be the scale factor that could be used to generate the dimensions of a room from the measurements on the blueprint?

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  32

  Pause and Reflect

  How is using scale factors to work with enlargements like using scale factors to work with reductions?

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  Enlargements and reductions generate similar figures. The scale factor relates the measurement of the original figure to those of the dilated figure in either case.

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  Practice

  

  Source: Muleshoe log cabin, Billy Hathom, Wikimedia Commons

  1. A replica of a log cabin at the Muleshoe Heritage Center in Muleshoe, Texas, has a blueprint with dimensions of 13 over 4 3 4 inches by 25 over 8 5 8 inches. According to the blueprint, 1 inch on the blueprint is equal to 8 feet on the actual structure. What are the dimensions in feet of the log cabin?

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     Use the scale factor to enlarge the dimensions from the blueprint to the dimensions of actual log cabin.

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  Source: Flickr - USCapitol - Stephen Austin Statue, Architect of the Capitol, Wikimedia Commons

  2. A sculptor often creates a small-scale version of a statue as a prototype before making the actual statue. A statue of Stephen F. Austin has a small-scale version with a height of 14 inches and a width of 31 over 2 1 2 inches. If the finished statue should have a height of 8 feet, what will be the width of the finished statue?

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     Set up and solve an equation of proportions. Be sure that your units of measure are the same. You may need to convert between feet and inches.

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  3. A blueprint shows that the dimensions of a rectangular game room are 31 over 4 1 4 inches by 57 over 8 7 8 inches, where 1 inch on the blueprint represents 4 feet in the actual room. What is the perimeter of the actual game room?

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     Use the scale factor to determine the dimensions of the actual game room, and then use those dimensions to determine the perimeter of the room.

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