Points A and B are at #(2 ,1 )# and #(3 ,5 )#, 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.
Aug 4, 2018

#C=(-1,-9)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

#A(2,1)toA'(1,-2)" where A' is the image of A"#

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

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

#ulb-ulc=2ula'-2ulc#

#ulc=2ula'-ulb#

#color(white)(ulc)=2((1),(-2))-((3),(5))#

#color(white)(ulc)=((2),(-4))-((3),(5))=((-1),(-9))#

#rArrC=(-1,-9)#

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