Points A and B are at #(1 ,7 )# and #(3 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?

1 Answer
Jim G.
May 1, 2018

#C=(8,-7/2)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

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

#rArrvec(CB)=color(red)(5)vec(CA')#

#rArrulb-ulc=5(ula'-ulc)#

#rArrulb-ulc=5ula'-5ulc#

#rArr4ulc=5ula'-ulb#

#color(white)(rArr4ulc)=5((7),(-1))-((3),(9))#

#color(white)(rArr4ulc)=((35),(-5))-((3),(9))=((32),(-14))#

#rArrulc=1/4((32),(-14))=((8),(-7/2))#

#rArrC=(8,-7/2)#

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