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Points A and B are at #(6 ,5 )# and #(7 ,8 )#, 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?

Answer 1

Ella Armstrong

#C=(-17,4)#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(6,5)toA'(-5,6)" 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((-5),(6))-((7),(8))#

#color(white)(rArrulc)=((-10),(12))-((7),(8))=((-17),(4))#

#rArrC=(-17,4)#

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