Points A and B are at #(2 ,4 )# and #(3 ,5 )#, 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
Feb 2, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(2,4)toA'(-4,2)" 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((-4),(2))-((3),(5))#
#color(white)(rArrulc)=((-8),(4))-((3),(5))=((-11),(-1))#
#rArrC=(-11,-1)#
