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Scale Factor of a Mug

Relationships between sides of similar figures

Scale factors and ratios are used to quantify the relationships between the sides of similar figures.

What is the scale factor from design Mug (x, y) to Roman (x+2, y-3)?

Comments for Scale Factor of a Mug

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Dec 13, 2012
Scale Factor
by: Staff


Part I


Your problem statement DOES NOT describe a change in the scale of the mug.

Your problem statement DOES describe a translation (of the location) of the Design Mug. It does not change the size of the design mug.

Design Mug (x, y) to Roman Mug (x+2, y-3) is merely a movement of the design mug to a new position.

The entire figure is merely shifted to the right by two units, and shifted down by three units.

The scale factor between the two figures = 1. There is no change in the size or shape of the mug.

Take a look at the following two diagrams. I have used a rectangle to represent the Design Mug, but any shape could be used.

Math – Design Mug (x,y)

Math - Roman Mug (x+2, y-3)


Dec 13, 2012
Scale Factor
by: Staff


Part II

Scale Factors

As already noted, scale factors are ratios which compare two objects. The scale factor often refers to a linear measurement (such as length and height). However, a scale factor can also refer to something else, such as area or volume.

For the purposes of this example, the scale factor refers to linear measurements.

The following diagram shows two Similar Rectangles. (Two figures are similar when the ratios of the lengths of their corresponding sides are equal.)

Math – Similar Geometric Figures

The linear scale factor of figure B compared to figure A is the ratio of the length of corresponding sides:

Scale Factor = (length of figure B) / (length of figure A)

Scale Factor = 4 / 8

Scale Factor = ½

The same scale factor can also be computed using the height of each figure:

Scale Factor = (height of figure B) / (height of figure A)

Scale Factor = 2 / 4

Scale Factor = ½

Every side of figure B is exactly ½ as long as the corresponding side of figure A.

Thanks for writing.


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