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

##### 1 Answer

May 18, 2018

#### Explanation:

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

#• " a point "(x,y)to(y,-x)#

#rArrA(7,3)toA'(3,-7)" where A' is the image of A"#

#rArrvec(CB)=color(red)(2)vec(CA')#

#rArrulb-ulc=2(ula'-ulc)#

#rArrulb-ulc=2ula'-2ulc#

#rArrulc=2ula'-ulb#

#color(white)(rArrulc)=2((3),(-7))-((3),(2))#

#color(white)(rArrulc)=((6),(-14))-((3),(2))=((3),(-16))#

#rArrC=(3,-16)#