# Points A and B are at #(6 ,1 )# and #(3 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?

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The coordinates of point C are (3, 5).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Points A and B are at #(2 ,7 )# and #(4 ,6 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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?
- Circle A has a radius of #2 # and a center of #(8 ,2 )#. Circle B has a radius of #4 # and a center of #(5 ,3 )#. If circle B is translated by #<-1 ,5 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(2 ,9 )# and #(3 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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?
- Point A is at #(5 ,-8 )# and point B is at #(-3 ,3 )#. Point A is rotated #pi/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Points A and B are at #(3 ,5 )# and #(6 ,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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