# Circle A has a radius of #3 # 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 #<2 ,7 >#, 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, require to find the 'new' centre of circle B under the given transformation which does not change the shape of the circle only it's position.

To calculate d, in this case since the coordinates of the centres (8 ,5) and (8 ,8) have the same x-coordinate- that is they lie on the same vertical line, then d is the difference in the y-coordinates.

Sum of radii = radius of A + radius of B = 3 + 2 + 5

Since sum of radii > d , then the circles overlap graph{(y^2-10y+x^2-16x+80)(y^2-16y+x^2-16x+124)=0 [-28.48, 28.48, -14.22, 14.26]}

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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 line segment has endpoints at #(9 ,6 )# and #(5 ,3)#. If the line segment is rotated about the origin by #pi #, translated vertically by #2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
- A line segment has endpoints at #(1 ,6 )# and #(6 ,7 )#. The line segment is dilated by a factor of #4 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?
- Circle A has a radius of #1 # and a center of #(1 ,2 )#. Circle B has a radius of #4 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,5 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- What are the coordinates of the image of the point #(–3, 6)# after a dilation with a center of #(0, 0)# and scale factor of #1/3#?
- A line segment has endpoints at #(5 ,8 )# and #(7 ,6)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #-3 #, and reflected about the y-axis, what will the line segment's new endpoints be?

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