Answer:
1. [tex]R_{90} (x,y)=(-y,x)[/tex]
2. [tex]R_{180} (x,y)=(-x,-y)[/tex]
3. [tex]R_{270} (x,y)=(y,-x)[/tex].
Step-by-step explanation:
Let us assume a point (x,y) in the co-ordinate plane on which the transformations will be applied.
Now, we know that 'rotation' is a transformation that turns that image to a certain degree about a point.
So, the given transformations gives us the forms as:
1. When we rotate an ( x,y ) by 90° about origin counter-clockwise, the resultant co-ordinate is ( -y,x ).
So, the function form is [tex]R_{90} (x,y)=(-y,x)[/tex].
2. When we rotate an ( x,y ) by 180° about origin counter-clockwise, the resultant co-ordinate is ( -x,-y ).
So, the function form is [tex]R_{180} (x,y)=(-x,-y)[/tex].
3. When we rotate an ( x,y ) by 270° about origin counter-clockwise, the resultant co-ordinate is ( y,-x ).
So, the function form is [tex]R_{270} (x,y)=(y,-x)[/tex].