When a shape is rotated, it must be rotated through a point
The new position of point B is point A
The angle of rotation is given as:
[tex]Angle = 288^o[/tex]
The shape is a regular pentagon (with 5 sides).
The smallest angle of rotation that maps the pentagon onto itself is calculated using:
[tex]\theta = \frac{360}n[/tex]
So, we have:
[tex]\theta = \frac{360}5[/tex]
[tex]\theta = 72[/tex]
Let the number of rotations be n.
So, we have:
[tex]\theta \times n= Angle[/tex]
This gives
[tex]72 \times n= 288[/tex]
Divide both sides by 72
[tex]n= 4[/tex]
This means that the new position of B is 4 points away from B.
Point A is 4 points away from B, in clockwise direction
Hence, the new position of point B is point A
Read more about rotation at:
https://brainly.com/question/2283733
