# Points A and B are at #(6 ,7 )# and #(3 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?

##### 1 Answer

we know , if in two dimension the rotation of a point **(x,y)** about origin by an angle **(x',y')** then

Here

So transformed coordinates of

Similarly transformed coordinates of

Let the coordinates of center of dilation C be (h,k).

So A' on 5 times dilation about C will be transformed into

By the given condition

So

Again

Hence coordinates of