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Points A and B are at #(8 ,2 )# and #(5 ,7 )#, 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

Violet Aldrich

#C=(-11/2,8)#

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

#• " a point "(x,y)to(-y,x)#

#A(8,2)toA'(-2,8)" 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((-2),(8))-((5),(7))#

#color(white)(rArr2ulc)=((-6),(24))-((5),(7))=((-11),(16))#

#rArrulc=1/2((-11),(16))=((-11/2,8))#

#rArrC=(-11/2,8)#

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Answer 2

Parker Allen

The coordinates of point C are (8, 5).

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Answer from HIX Tutor

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