# Points A and B are at #(6 ,5 )# and #(7 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # 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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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.

- Circle A has a radius of #1 # and a center at #(3 ,3 )#. Circle B has a radius of #3 # and a center at #(1 ,7 )#. If circle B is translated by #<2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A line segment has endpoints at #(7 ,9 )# and #(5 ,2)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-4 #, and reflected about the x-axis, what will the line segment's new endpoints be?
- A triangle has corners at #(1 ,3 )#, #(9 ,4 )#, and #(2 ,2 )#. If the triangle is dilated by a factor of #2 # about point #(9 ,5 ), how far will its centroid move?
- A line segment has endpoints at #(7 ,8 )# and #(3 ,5 )#. If the line segment is rotated about the origin by #(3 pi)/2 #, translated vertically by #-2 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- Circle A has a radius of #3 # and a center of #(3 ,3 )#. Circle B has a radius of #5 # and a center of #(1 ,7 )#. If circle B is translated by #<2 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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