Points A and B are at #(3 ,8 )# and #(7 ,3 )#, 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
Jul 31, 2018

#C=(-11/2,-43/4)#

Explanation:

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

#• " a point "(x,y)to(-x,-y)#

#A(3,8)toA'(-3,-8)" 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),(-8))-((7),(3))#

#color(white)(4ulc)=((-15),(-40))-((7),(3))=((-22),(-43))#

#ulc=1/4((-22),(-43))=((-11/2),(-43/4))#

#rArrC=(-11/2,-43/4)#