When a shape is rotated, it must be rotated through a point.
The radius of the circle is: 4
The location of point F is:
[tex]F = (4,0)[/tex]
When the shape is rotated [tex]90^o[/tex] counterclockwise, the rule is:
[tex](x,y) \to (-y,x)[/tex]
So, the location of point F' is:
[tex]F' = (0,4)[/tex]
The center of the circle is given as:
[tex]O = (0,0)[/tex]
The radius of the circle is the distance from the center to point F or F'
This is calculated using the following distance formula
[tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
The distance from O to F is:
[tex]r =\sqrt{(0 - 4)^2 + (0 - 0)^2}[/tex]
[tex]r =\sqrt{16 + 0}[/tex]
[tex]r =\sqrt{16}[/tex]
Take square roots
[tex]r = \±4[/tex]
Radius cannot be negative.
So:
[tex]r = 4[/tex]
Hence, the radius of the circle is (b) 4
Read more about rotation at:
https://brainly.com/question/1571997
