Points A and B are at #(8 ,3 )# and #(5 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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 8, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#A(8,3)toA'(-3,8)" where A' is the image of A"#
#vec(CB)=color(red)(2)vec(CA')#
#ulb-ulc=2(ula'-ulc)#
#ulb-ulc=2ula'-2ulc#
#ulc=2ula'-ulb#
#color(white)(ulc)=2((-3),(8))-((5),(4))#
#color(white)(ulc)=((-6),(16))-((5),(4))=((-11),(12))#
#rArrC=(-11,12)#
