# Circle A has a radius of #1 # and a center of #(5 ,2 )#. Circle B has a radius of #2 # and a center of #(4 ,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?

After the translation

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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 #3 #. If point A is now at point B, what are the coordinates of point C?
- A line segment with endpoints at #(-3 , 6 )# and #(-5, 1 )# is rotated clockwise by #pi #. What are the new endpoints of the line segment?
- Points A and B are at #(6 ,7 )# and #(3 ,9 )#, 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?
- A triangle has corners at #(1, 2 )#, ( 1 , -9)#, and #( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- Points A and B are at #(9 ,4 )# and #(1 ,2 )#, 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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