# Circle A has a radius of #3 # and a center of #(2 ,7 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

The circles do not overlap and the minimum distance is

The equation of the circle after translation is

This distance is greater than the sum of the radii

So, the circles do not overlap and the minimum distance is

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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.

- A triangle has corners at #(1 ,3 )#, #(2 ,-2 )#, and #(-8 ,6 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,2 ), how far will its centroid move?
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- Point A is at #(1 ,-9 )# and point B is at #(-2 ,8 )#. Point A is rotated #(3pi)/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?
- Pre-image: A(−4, 2) , B(4, 4) , and C(−1, 2) Image: A′(−2, 1) , B′(2, 2) , and C′(−12, 1) Is the dilation an expansion or contraction? What is the scale factor?
- Circle A has a radius of #2 # and a center of #(7 ,6 )#. Circle B has a radius of #3 # and a center of #(5 ,3 )#. If circle B is translated by #<-1 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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