Points A and B are at #(7 ,1 )# and #(3 ,7 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?

1 Answer
Apr 20, 2018

#C=(-12,-5)#

Explanation:

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

#• " a point "(x,y)to(-x,-y)#

#rArrA(7,1)toA'(-7,-1)" where A' is the image of A"#

#rArrvec(CB)=color(red)(3)vec(CA')#

#rArrulb-ulc=3(ula'-ulc)#

#rArrulb-ulc=3ula'-3ulc#

#rArr2ulc=3ula'-ulb#

#color(white)(rArr2ulc)=3((-7),(-1))-((3),(7))#

#color(white)(rArr2ulc)=((-21),(-3))-((3),(7))=((-24),(-10))#

#rArrulc=1/2((-24),(-10))=((-12),(-5))#

#rArrC=(-12,-5)#