Points A and B are at #(6 ,1 )# and #(8 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2017-05-28T07:06:26

The point #C=(-20,-11)#

A rotation counterclockwise by #pi#, point #A# becomes #A'#

#A=(6,1)#

The coordinates of #A'=(-6,-1)#

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

So,

#vec(CB)=2vec(CA')#

#((8-x),(9-y))=2((-6-x),(-1-y))#

Therefore,

#8-x=-12-2x#, #=>#, #x=-12-8=-20#

#9-y=-2-2y#, #=>#, #y=-2-9=-11#

The point #C=(-20,-11)#