Points A and B are at #(9 ,4 )# and #(1 ,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?

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Answer 1 · 2017-08-12T11:57:03

The coordinates of #C=(11/2,-16)#

Point #A=((9),(4))# and point #B=((1),(5))#

The rotation of point #A# counterclockwise by #(3/2pi)# tranforms the point #A# into

#A'=((4),(-9))#

Let point #C=((x),(y))#

The dilatation is

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

#((1),(5))-((x),(y))=3*((4),(-9))-((x),(y)))#

Therefore,

#1-x=3(4-x)#

#1-x=12-3x#

#2x=12-1=11#, #=>#, #x=11/2#

#5-y=3(-9-y)#

#5-y=-27-3y#

#2y=-27-5=-32#, #=>#, #y=-16#

The point #C=(11/2,-16)#