Points A and B are at #(7 ,3 )# and #(5 ,9 )#, 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 21, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#A(7,3)toA'(3,-7)#
#vec(CB)=color(red)(2)vec(CA')#
#ulb-ulc=2(ula'-ulc)#
#ulb-ulc=2ula'-2ulc#
#ulc=2ula'-ulb#
#color(white)(ulc)=2((3),(-7))-((5),(9))#
#color(white)(ulc)=((6),(-14))-((5),(9))=((1),(-23))#
#rArrC=(1,-23)#
