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 #2 #. If point A is now at point B, what are the coordinates of point C?
1 Answer
May 26, 2018
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)(2)vec(CA')#
#ulb-ulc=2(ula'-ulc)#
#ulb-ulc=2ula'-2ulc#
#ulc=2ula'-ulb#
#color(white)(ulc)=2((4),(-9))-((7),(2))#
#color(white)(ulc)=((8),(-18))-((7),(2))=((1),(-20))#
#C=(1,-20)#
