Points A and B are at #(9 ,7 )# and #(8 ,6 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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 22, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "pi#
#• " a point "(x,y)to(-x,-y)#
#A(9,7)toA'(-9,-7)" 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((-9),(-7))-((8),(6))#
#color(white)(ulc)=((-18),(-14))-((8),(6))=((-26),(-20))#
#rArrC=(-26,-20)#
