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Points A and B are at #(6 ,1 )# and #(3 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?

Answer 1

Maverick Smith

#C=(1/2,-35/4)#

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

#• " a point "(x,y)to(y,-x)#

#A(6,1)toA'(1,-6)" where A' is the image of A"#

#vec(CB)=color(red)(5)vec(CA')#

#ulb-ulc=5(ula'-ulc)#

#ulb-ulc=5ula'-5ulc#

#4ulc=5ula'-ulb#

#color(white)(4ulc)=5((1),(-6))-((3),(5))#

#color(white)(4ulc)=((5),(-30))-((3),(5))=((2),(-35))#

#ulc=1/4((2),(-35))=((1/2),(-35/4))#

#rArrC=(1/2,-35/4)#

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Answer 2

Jayden Jackson

The coordinates of point C are (3, 5).

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Answer from HIX Tutor

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