# Points A and B are at #(7 ,9 )# and #(6 ,8 )#, 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

Jun 27, 2018

#### Explanation:

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

#• " a point "(x,y)to(y,-x)#

#A(7,9)toA'(9,-7)" where A' is the image of A"#

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

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

#ulb-ulc=2ula'-2ulc#

#ulc=2ula'-ulb#

#color(white)(ulc)=2((9),(-7))-((6),(8))#

#color(white)(ulc)=((18),(-14))-((6),(8))=((12),(-22))#

#rArrC=(12,-22)#