Points A and B are at #(4 ,3 )# and #(5 ,2 )#, 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?

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Jim G. Share
Feb 28, 2018

Answer:

#C=(1,-10)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

#rArrA(4,3)toA'(3,-4)" 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((3),(-4))-((5),(2))#

#color(white)(rArrulc)=((6),(-8))-((5),(2))=((1),(-10))#

#rArrC=(1,-10)#

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