In most cases; when an object is transformed, the position of the object changes. A clockwise rotation of 144 degrees about the origin will map the pentagon onto itself.
Given:
The attached pentagon
The number of sides (n) in a pentagon is:
[tex]n = 5[/tex]
The pentagon will not be mapped onto itself when reflected across line m because m is not at the center of the polygon
The pentagon will not be mapped onto itself when reflected across the x-axis because the pentagon has 5 sides (odd number of sides)
To map the pentagon onto itself, the pentagon has to be rotated.
The angle of rotation is:
[tex]\theta = \frac{360}n[/tex]
[tex]\theta = \frac{360}5[/tex]
[tex]\theta = 72[/tex]
Other possible angles of rotation must be a multiple of 72. i.e.
[tex]\theta = 72, 144, 216, 288....[/tex]
This means that: option (d) is correct because 144 is a multiple of 72
Hence, a clockwise rotation of 144 degrees about the origin will map the pentagon onto itself.
Read more about transformation at:
brainly.com/question/24326503
