Question

Circle A has been enlarged to create circle A'. The table below shows the circumference of both circles.

Circumference
Circle
Circumference (inches)
А
7
A
10.5
Based on the information in the table, what scale factor was used to create circle A?
:.67
.: 1.5
:: 73.5
1
2
3
4 5 6
Next

Answer 1

Option (2) 1.5

Explanation:

Rule for the dilation of an image by a scale factor is,

Scale factor =
`\frac{\text{Radius of image circle A'}}{\text{Radius of pre-image A}}=(r')/(r)`

=
`((2\pi) r')/((2\pi) r)`

=
`\frac{\text{Circumference of image}}{\text{Circumference of pre-image}}`

=
`(10.5)/(7)`

= 1.5

Therefore, scale factor was used to create a circle A' = 1.5

Option (2) will be the correct option.