Points A and B are at #(8 ,5 )# and #(2 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # 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
Jim G.
Feb 27, 2018

#C=(13/2,-13)#

Explanation:

#"under a counterclockwise rotation about the origin of "(3pi)/2#

#• " a point "(x,y)to(y,-x)#

#rArrA(8,5)toA'(5,-8)" 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((5),(-8))-((2),(2))#

#color(white)(rArr2ulc)=((15),(-24))-((2),(2))=((13),(-26))#

#rArrulc=1/2((-13),(-26))=((13/2),(-13))#

#rArrC=(13/2,-13)#

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