Points A and B are at #(1 ,8 )# and #(3 ,6 )#, 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.
Sep 9, 2017

#C=(13,-8)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

#rArrA(1,8)toA'(8,-1)" where A' is the image of A"#

#"under a dilatation about C of factor 2"#

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

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

#rArrulc=2ula'-ulb#

#color(white)(rArrulc)=2((8),(-1))-((3),(6))#

#color(white)(rArrulc)=((16),(-2))-((3),(6))=((13),(-8))#

#rArrC=(13,-8)#

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