Points A and B are at #(4 ,9 )# and #(6 ,8 )#, 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
Apr 20, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(4,9)toA'(9,-4)" where A' is the image of A"#
#rArrvec(CB)=color(red)(2)vec(CA')#
#rArrulb-ulc=2(ula'-ulc)#
#rArrulb-ulc=2ula'-2ulc#
#rArrulc=2ula'-ulb#
#color(white)(rArrulc)=2((9),(-4))-((6),(8))#
#color(white)(rArrulc)=((18),(-8))-((6),(8))=((12),(-16))#
#rArrC=(12,-16)#
