Question

Can someone please help?!

Answer 1

Answer:

1. $R_{90} (x,y)=(-y,x)$

2. $R_{180} (x,y)=(-x,-y)$

3. $R_{270} (x,y)=(y,-x)$.

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 $R_{90} (x,y)=(-y,x)$.

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 $R_{180} (x,y)=(-x,-y)$.

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 $R_{270} (x,y)=(y,-x)$.