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Creating Scale Drawings

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Learning Targets

When I know the actual measurements, I can create a scale drawing at a given scale.
I know how different scales affect the lengths in the scale drawing.
I can determine the scale of a scale drawing when I know lengths on the drawing and corresponding actual lengths.

Notes

If we want to create a scale drawing of a room's floor plan that has the scale “1 inch to 4 feet,” we can divide the actual lengths in the room (in feet) by 4 to find the corresponding lengths (in inches) for our drawing.

Suppose the longest wall is 15 feet long. We should draw a line 3.75 inches long to represent this wall, because 15÷4=3.75.

There is more than one way to express this scale.

These three scales are all equivalent, since they represent the same relationship between lengths on a drawing and actual lengths:

1 inch to 4 feet
½ inch to 2 feet
¼ inch to 1 foot

Any of these scales can be used to find actual lengths and scaled lengths (lengths on a drawing). For instance, we can tell that, at this scale, an 8-foot long wall should be 2 inches long on the drawing because ¼ ⋅ 8 = 2.

The size of a scale drawing is influenced by the choice of scale. For example, here is another scale drawing of the same room using the scale 1 inch to 8 feet.

Notice this drawing is smaller than the previous one. Since one inch on this drawing represents twice as much actual distance, each side length only needs to be half as long as it was in the first scale drawing.

Construct scale drawingsAn urban planner needs your help in creating a scale drawing. Let's use our knowledge about scale factor, length, and area to assist.

Activity

9.2 Bedroom Floor Plan

What is a floor plan?

A floor plan is a top-view drawing that shows a layout of a room or building.

They’re usually scale drawings.

Sometimes the scale isn’t noted, but we can find it if we know the scaled and actual lengths.

Here is a rough sketch of Noah’s bedroom. (not a scale drawing).

Noah wants to create a floor plan that is a scaled drawing. The actual length of Wall C is 4 m. Noah draws a segment 16 cm long to represent Wall C. What scale is he using? Explain or show your reasoning.
Find another way to express the scale.
Pause and think. How do your scales compare?
The actual lengths of Wall A, Wall B, and Wall D are 2.5 m, 2.75 m, and 3.75 m. Determine how long these walls will be on Noah’s scale floor plan.
Use the Point tool and the Segment tool to draw the walls of Noah's scale floor plan in the applet below.

7.1.8.2 Bedroom Floor Plan7.1.8.2 Bedroom Floor Plan

Add To Your Notes

Even if we express a scale in lots of equivalent ways...

scales are often simplified to show the actual distance for 1 scaled unit (example: 1 cm to 0.25 m)
it is common to express at least one distance as a whole number or a benchmark fraction (like ¼, ½)

9.3 Two Maps of Utah

A rectangle around Utah is about 270 miles wide and about 350 miles tall. The upper right corner that is missing is about 110 miles wide and about 70 miles tall.

In your notes, make a scale drawing of Utah where 1 centimeter represents 50 miles.
In your notes, make a scale drawing of Utah where 1 centimeter represents 75 miles.

How do the two drawings compare? How does the choice of scale influence the drawing?

Add To Your Notes

The size of the scale determines the size of the drawing. You can have different-sized scale drawings of the same actual object, but the size of the actual object doesn’t change.

“Suppose there are two scale drawings of the same house. One uses the scale of 1 cm to 2 m, and the other uses the scale 1 cm to 4 m. Which drawing is larger? Why?” (The one with the 1 cm to 2 m scale is larger, because it takes 2 cm on the drawing to represent 4 m of actual length.)
“Another scale drawing of the house uses the scale of 5 cm to 10 m. How does its size compare to the other two?” (It is the same size as the drawing with the 1 cm to 2 m scale.)

Sometimes two different scales are actually equivalent, such as 5 cm to 10 m and 1 cm to 2 m. It is common to write a scale so that it tells you what one unit on the scale drawing represents (for example, 1 cm to 2 m).

Summary

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