# Points A and B are at #(1 ,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 #4 #. If point A is now at point B, what are the coordinates of point C?

##### 1 Answer

Jul 31, 2018

#### Explanation:

#"under a counterclockwise rotation about the origin of "(3pi)/2#

#• " a point "(x,y)to(y,-x)#

#A(1,7)toA'(7,-1)" where A' is the image of A"#

#vec(CB)=color(red)(4)vec(CA')#

#ulb-ulc=4(ula'-ulc)#

#ulb-ulc=4ula'-4ulc#

#3ulc=4ula'-ulb#

#color(white)(3ulc)=4((7),(-1))-((3),(9))#

#color(white)(3ulc)=((28),(-4))-((3),(9))=((25),(-13))#

#ulc=1/3((25),(-13))=((25/3),(-13/3))#

#rArrC=(25/3,-13/3)#