Points A and B are at #(8 ,5 )# and #(8 ,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
Explanation:
#"under a counterclockwise rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#A(8,5)toA'(5,-8)" 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((5),(-8))-((8),(2))#
#color(white)(2ulc)=((15),(-24))-((8),(2))=((7),(-26))#
#ulc=1/2((7),(-26))=((7/2),(-13))#
#rArrC=(7/2,-13)#
