Points A and B are at #(4 ,9 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

1 Answer
Jan 24, 2018

#C=(5,14)#

Explanation:

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

#• " a point "(x,y)to(y,-x)#

#rArrA(4,9)toA'(9,-4)" where A' is the image of A"#

#rArrvec(CB)=color(red)(1/2)vec(CA')#

#rArrulb-ulc=1/2(ula'-ulc)=1/2ula'-1/2ulc#

#rArr-1/2ulc=1/2a'-ulb#

#color(white)(xxxxxx)=1/2((9),(-4))-((7),(5))=((-5/2),(-7))#

#rArrulc=-2((-5/2),(-7))=((5),(14))#

#rArrC=(5,14)#