Points A and B are at #(4 ,1 )# 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
May 11, 2018

#C=(1/3,-25/3)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

#rArrA(4,1)toA'(1,-4)" where A' is the image of A"#

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

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

#rArrulb-ulc=4ula'-4ulc#

#rArr3ulc=4ula'-ulb#

#color(white)(rArr3ulc)=4((1),(-4))-((3),(9))#

#color(white)(rArr3ulc)=((4),(-16))-((3),(9))=((1),(-25))#

#rArrulc=1/3((1),(-25))=((1/3),(-25/3))#

#rArrC=(1/3,-25/3)#