Circle A has a radius of #2 # and a center of #(6 ,5 )#. Circle B has a radius of #3 # and a center of #(2 ,4 )#. If circle B is translated by #<1 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
Circle B overlaps circle A after translation.
If circle B is translated by <
Let circle B' has a radius of
The distance Let This satisfies the inequation: Therefore circle A and circle B' (translated circle B) do neither circumscribe nor inscribe. They overlap. By signing up, you agree to our Terms of Service and Privacy Policy
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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.
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 #(6, 3 )#, ( 8, -2)#, and #(1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- Points A and B are at #(4 ,1 )# and #(8 ,3 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?
- Circle A has a radius of #5 # 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?
- Using the graph of f(x)= 1/x as a starting point, describe the transformations to get to #g(x) = 1/x-4#?
- A line segment has endpoints at #(2 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #3 # around #(6 , 4)#. What are the new endpoints and length of the line segment?

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