Points A and B are at #(2 ,9 )# and #(8 ,6 )#, 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
Feb 5, 2018

#C=(-16/3,-14)#

Explanation:

#"under a counterclockwise rotation about the origin of "pi#

#• " a point "(x,y)to(-x-y)#

#rArrA(2,9)toA'(-2,-9)" 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)(rArr3ulc)=4((-2),(-9))-((8),(6))#

#color(white)(rArr3ulc)=((-8),(-36))-((8),(6))=((-16),(-42))#

#rArrulc=1/3((-16),(-42))=((-16/3),(-14))#

#rArrC=(-16/3,-14)#