Points A and B are at #(8 ,5 )# and #(2 ,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
Feb 27, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(8,5)toA'(5,-8)" where A' is the image of A"#
#rArrvec(CB)=color(red)(3)vec(CA')#
#rArrulb-ulc=3(ula'-ulc)#
#rArrulb-ulc=3ula'-3ulc#
#rArr2ulc=3ula'-ulb#
#color(white)(rArr2ulc)=3((5),(-8))-((2),(2))#
#color(white)(rArr2ulc)=((15),(-24))-((2),(2))=((13),(-26))#
#rArrulc=1/2((-13),(-26))=((13/2),(-13))#
#rArrC=(13/2,-13)#
