Points A and B are at #(9 ,7 )# and #(2 ,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
Jul 9, 2017

#C=(-23/2,11)#

Explanation:

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

#• " a point " (x,y)to(-y,x)#

#rArrA(9,7)toA'(-7,9)"where " A' " is the image of A"#

#"under a dilatation about C of factor 3"#

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

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

.#rArr2ulc=3ula'-ulb#

#color(white)(rArr2)=3((-7),(9))-((2),(5))=((-21),(27))-((2),(5))#

#rArrulc=1/2((-23),(22))#

#color(white)(xxxx)=((-23/2),(11))#

#"the components of "ulc" are the coordinates of C"#

#rArrC=(-23/2,11)#