Points A and B are at #(9 ,7 )# and #(4 ,3 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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 · 2016-10-02T21:17:06

#C = (-31/3, -8)#

Let's begin by rotating point A:

#r = sqrt(9² + 7²)#

#r = sqrt(81 + 49)#

#r = sqrt130#

#theta = tan^-1(7/9) + pi#

The new point A is:

#(sqrt130cos(tan^-1(7/9) + pi), sqrt130sin(tan^-1(7/9) + pi))#

#(-9, -7)#

#4 = 3(9 - C_x)#

#3 = 3(7 - C_y)#

#C_x = -9 - 4/3 = -31/3#

#C_y = -7 - 1 = -8#

#C = (-31/3, -8)#