Points A and B are at #(4 ,9 )# and #(6 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2017-06-15T18:37:26

The point #C=(10,-8)#

The matrix of a rotation counterclockwise by #3/2pi# about the origin is

#((0,1),(-1,0))#

Therefore, the transformation of point #A# is

#A'=((0,1),(-1,0))((4),(9))=((9),(-4))#

Let point #C# be #(x,y)#, then

#vec(CB)=4 vec(CA')#

#((6-x),(8-y))=4((9-x),(-4-y))#

So,

#6-x=3(9-x)#

#6-x=36-4x#

#3x=30#

#x=10#

and

#8-y=4(-4-y)#

#8-y=-16-4y#

#3y=-24#

#y=-8#

Therefore,

point #C=(10,-8)#