Points A and B are at #(5 ,8 )# and #(3 ,2 )#, 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?

1 Answer
Jul 6, 2018

#C=(-27/2,13/2)#

Explanation:

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

#• " a point "(x,y)to(-y,x)#

#A(5,8)toA'(-8,5)" where A' is the image of A"#

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

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

#ulb-ulc=3ula'-3ulc#

#2ulc=3ula'-ulb#

#color(white)(2ulc)=3((-8),(5))-((3),(2))#

#color(white)(2ulc)=((-24),(15))-((3),(2))=((-27),(13))#

#ulc=1/2((-27),(13))=((-27/2),(13/2))#

#rArrC=(-27/2,13/2)#