Points A and B are at #(1 ,1 )# and #(4 ,7 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?

1 Answer
Jim G.
Apr 1, 2018

#C=(-2,-9)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

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

#rArrvec(CB)=color(red)(2)vec(CA')#

#rArrulb-ulc=2(ula'-ulc)#

#rArrulb-ulc=2ula'-2ulc#

#rArrulc=2ula'-ulb#

#color(white)(rArrulc)=2((1),(-1))-((4),(7))#

#color(white)(rArrulc)=((2),(-2))-((4),(7))=((-2),(-9))#

#rArrC=(-2,-9)#

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