Scale Factor and Proportions

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, a quantity. It is used to determine how much larger or smaller a figure is compared to another figure.

Front

How do you find the scale factor between two similar figures?

Back

To find the scale factor, divide the length of a side of the larger figure by the length of the corresponding side of the smaller figure.

Front

If the scale factor from ΔDEF to ΔABC is 1/2, what does this mean?

Back

It means that each side of ΔDEF is half the length of the corresponding side of ΔABC.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and then solve for the unknown variable.

Front

If 3/4 = x/16, what is the value of x?

Back

x = 12 (cross-multiply: 3 * 16 = 4 * x).

Front

What is the relationship between scale factors and proportions?

Back

Scale factors can be expressed as proportions, showing the relationship between corresponding sides of similar figures.

Front

If a triangle has sides of 6, 8, and 10, and is scaled by a factor of 2, what are the new side lengths?

Back

The new side lengths are 12, 16, and 20.

Front

What does it mean to 'solve for x' in a proportion?

Back

It means to find the value of x that makes the proportion true.

Front

If 5/x = 10/20, what is the value of x?

Back

x = 10 (cross-multiply: 5 * 20 = 10 * x).