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Points A and B are at #(2 ,9 )# and #(3 ,1 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?

Answer 1

Jayden Jackson

#C=(-15,5/2)#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(2,9)toA'(-9,2)" where A' is the image of A"#

#rArrvec(CB)=color(red)(3)vec(CA')#

#rArrulb-ulc=3(ula'-ulc)#

#rArrulb-ulc=3ula'-3ulc#

#rArr2ulc=3ula'-ulb#

#color(white)(rArr2ulc)=3((-9),(2))-((3),(1))#

#color(white)(rArr2ulc)=((-27),(6))-((3),(1))=((-30),(5))#

#rArrulc=1/2((-30),(5))=((-15),(5/2))#

#rArrC=(-15,5/2)#

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Answer 2

Wyatt Anderson

The coordinates of point C are (-11, 9).

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Answer from HIX Tutor

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