Scale Factors

Question 1

What is a scale factor?

Answer 1

A scale factor is a number that scales, or multiplies, a quantity. It determines how much a figure is enlarged or reduced.

Question 2

How do you find the scale factor when comparing two similar figures?

Answer 2

The scale factor is found by dividing the length of a side of one figure by the corresponding side of the other figure.

Question 3

If a shape is scaled by a factor of 2, how does its size change?

Answer 3

The shape becomes twice as large, increasing all dimensions proportionally.

Question 4

If a rectangle has a length of 4 cm and a width of 2 cm, what are the dimensions if it is scaled by a factor of 1.5?

Answer 4

The new dimensions would be 6 cm (length: 4 cm * 1.5) and 3 cm (width: 2 cm * 1.5).

Question 5

What is the scale factor if a triangle with a base of 5 cm and a height of 10 cm is reduced to a base of 2.5 cm and a height of 5 cm?

Answer 5

The scale factor is 0.5, since both dimensions are halved.

Question 6

Can scale factors be negative?

Answer 6

No, scale factors are always positive since they represent a ratio of lengths.

Question 7

How do scale factors affect volumes?

Answer 7

When a three-dimensional shape is scaled by a factor of (k), the volume is scaled by (k^3).

Question 8

What is an example of a real-world application of scale factors?

Answer 8

Scale factors are often used in maps and architectural drawings to represent larger areas or buildings at a manageable size.

Question 9

What is the relationship between the scale factor and the corresponding sides of similar figures?

Answer 9

The ratio of any two corresponding sides of similar figures will always be equal to the scale factor.