Question

Shelley wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.

Answer 1

Given an object with perimeter a, if we apply a scale factor of 2, the new perimeter would be a * 2 = 2a

Also, for an object with area b, if we apply a scale factor of 2, the new area would be b * 2^2 = 4b

Considering the given scenario,

For a scale factor of 5,

Perimeter of image = 5 x perimeter of pre-image

Area of image = 5^2 x area of pre-image = 25 x area of pre-image

For a scale factor of 6,

Perimeter of image = 6 x perimeter of pre-image

Area of image = 6^2 x area of pre-image = 36 x area of pre-image