Points A and B are at #(9 ,7 )# and #(3 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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.
Feb 17, 2018

#C=(-17,14)#

Explanation:

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

#• " a point "(x,y)to(-y,x)#

#rArrA(9,7)toA'(-7,9)" 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((-7),(9))-((3),(4))#

#color(white)(rArrulc)=((-14),(18))-((3),(4))=((-17),(14))#

#rArrC=(-17,14)#

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