Points A and B are at #(2 ,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 28, 2018

#C=(23,8)#

Explanation:

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

#• " a point "(x,y)to(-y,x)#

#rArrA(2,9)toA'(-9,2)" where A' is the image of A"#

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

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

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

#rArr1/2ulc=ulb-1/2ula'#

#color(white)(rArr1/2ulc)=((7),(5))-1/2((-9),(2))#

#color(white)(rArr1/2ulc)=((7),(5))-((-9/2),(1))=((23/2),(4))#

#rArrulc=2((23/2),(4))=((23),(8))#

#rArrC=(23,8)#