In geometry, transformations are used to move a point or points from one position to another. The transformation of [tex](x,y) \to (-y,x)[/tex] is a 90 degrees rotation about the origin.
Given that:
[tex]A(-1,1) \to A'(-1,-1)[/tex]
[tex]B(1,1) \to B'(-1,1)[/tex]
[tex]C(1,4) \to C'(-4,1)[/tex]
The transformation rule is:
[tex](x,y) \to (-y,x)[/tex]
When a point is rotated through [tex](x,y) \to (-y,x)[/tex]
Such point has undergone a 90 degrees counterclockwise rotation.
Hence, option (a) is correct.
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