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

Apr 1, 2018

#### Explanation:

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

#• " a point "(x,y)to(y,-x)#

#rArrA(3,5)toA'(5,-3)" where A' is the image of A"#

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

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

#rArrulb-ulc=3ula'-3ulc#

#rArr2ulc=3ula'-ulb#

#color(white)(rArr2ulc)=3((5),(-3))-((6),(5))#

#color(white)(rArr2ulc)=((15),(-9))-((6),(5))=((9),(-14))#

#rArrulc=1/2((9),(-14))=((9/2),(-7))#

#rArrC=(9/2,-7)#