# Circle A has a radius of #3 # and a center of #(3 ,2 )#. Circle B has a radius of #5 # and a center of #(4 ,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?

circles overlap.

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

Before calculating d, we require to find the new centre of B under the given translation which does not change the shape of the circle, only it's position.

The 2 points here are (3 ,2) and (6 ,6)

Sum of radii = radius of A + radius of B =3 + 5 =8

Since sum of radii > d , then circles overlap graph{(y^2-4y+x^2-6x+4)(y^2-12y+x^2-12x+47)=0 [-22.5, 22.5, -11.25, 11.25]}

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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 #2 # and a center at #(5 ,6 )#. Circle B has a radius of #5 # and a center at #(2 ,4 )#. 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?
- Point A is at #(5 ,1 )# and point B is at #(2 ,-4 )#. 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?
- A line segment has endpoints at #(7 ,2 )# and #(3 , 2 )#. If the line segment is rotated about the origin by #(3 pi ) /2 #, translated vertically by # -4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- A triangle has corners at #(3, 5 )#, ( 6, 2)#, and #( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A line segment has endpoints at #(5 ,3 )# and #(5 ,4)#. If the line segment is rotated about the origin by #pi /2 #, translated horizontally by #-1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

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