When a shape is rotated, it must be rotated around a point.
See attachment for the image of each rotation.
To do this, the top coordinates of the X shape will be transformed using the appropriate rotation rule; the same rule will then be applied to the other parts of the X shape.
The top coordinates of the X shape are:
[tex]A = (0,0)[/tex]
[tex]B = (1,0)[/tex]
[tex]C = (3,0)[/tex]
[tex]D =(4,0)[/tex]
For 90 degrees counterclockwise rotation, the rule is:
[tex](x,y) \to (-y,x)[/tex]
So, we have:
[tex]A' = (0,0)[/tex]
[tex]B' = (0,1)[/tex]
[tex]C' = (0,3)[/tex]
[tex]D' = (0,4)[/tex]
For 180 degrees rotation, the rule is:
[tex](x,y) \to (-x,-y)[/tex]
So, we have:
[tex]A' = (0,0)[/tex]
[tex]B' = (-1,0)[/tex]
[tex]C' = (-3,0)[/tex]
[tex]D' = (-4,0)[/tex]
For 270 degrees counter rotation, the rule is:
[tex](x,y) \to (y,-x)[/tex]
So, we have:
[tex]A' = (0,0)[/tex]
[tex]B' = (0,-1)[/tex]
[tex]C' = (0,-3)[/tex]
[tex]D' = (0,-4)[/tex]
See attachment for the image of each rotation
Read more about rotations at:
https://brainly.com/question/1571997