Points A and B are at #(3 ,6 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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?

1 Answer
Jim G.
Jun 11, 2018

#C=(-11/2,-35/4)#

Explanation:

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

#• " a point "(x,y)to(-x,-y)#

#A(3,6)toA'(-3,-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((-3),(-6))-((7),(5))#

#color(white)(4ulc)=((-15),(-30))-((7),(5))=((-22),(-35))#

#ulc=1/4((-22),(-35))=((-11/2),(-35/4))#

#rArrC=(-11/2,-35/4)#

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