Points A and B are at #(9 ,4 )# and #(7 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?

1 Answer
May 28, 2018

#C=(5/2,-29/2)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

#A(9,4)toA'(4,-9)" where A' is the image of A"#

#vec(CB)=color(red)(3)vec(CA')#

#ulb-ulc=3(ula'-ulc)#

#ulb-ulc=3ula'-3ulc#

#2ulc=3ula'-ulb#

#color(white)(2ulc)=3((4),(-9))-((7),(2))#

#color(white)(2ulc)=((12),(-27))-((7),(2))=((5),(-29))#

#ulc=1/2((5),(-29))=((5/2),(-29/2))#

#rArrC=(5/2,-29/2)#