Points A and B are at #(5 ,8 )# and #(8 ,1 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?
1 Answer
Jan 14, 2018
Explanation:
#"under a counterclockwise rotation about the origin of "pi#
#• " a point "(x,y)to(-x-y)#
#rArrA(5,8)toA'(-8,-5)" where A' is the image of A"#
#rArrvec(CB)=color(red)(4)vec(CA')#
#rArrulb-ulc=4(ula'-ulc)#
#rArrulb-ulc=4ula'-4ulc#
#rArr3ulc=4ula'-ulb#
#color(white)(rArrul3c)=4((-8),(-5))-((8),(1))#
#color(white)(rArrul3c)=((-32),(-20))-((8),(1))=((-40),(-21))#
#rArrulc=1/3((-40),(-21))=((-40/3),(-7))#
#rArrC=(-40/3,-7)#
