# Circle A has a radius of #1 # and a center at #(7 ,4 )#. Circle B has a radius of #3 # and a center at #(6 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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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 #3 # and a center at #(1 ,3 )#. Circle B has a radius of #5 # 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?
- Points A and B are at #(2 ,9 )# and #(8 ,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?
- A line segment with endpoints at #(1 , -2 )# and #(6, -7 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?
- Circle A has a radius of #4 # and a center of #(8 ,5 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<3 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- How do you reflect across the y-axis the points F(-5, 1), x(-3, 3), E-1,-1)?

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