# Circle A has a radius of #4 # and a center of #(5 ,3 )#. Circle B has a radius of #2 # and a center of #(1 ,2 )#. If circle B is translated by #<2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

circles overlap.

What we have to do here is compare the distance ( d) between the centres of the circles with the sum of the radii.

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

The first step is to calculate the coordinates of the 'new' centre of circle B under the given translation. Under a translation the circle remains a circle but it's position changes.

(1 ,2) → (1+2 ,2+4) → new centre of B is (3 ,6)

Here the 2 points are (5 ,3) and (3 ,6) the centres of the circles.

sum of radii = radius of A + radius of B = 4 + 2 = 6

Since sum of radii > d , then circles overlap graph{(y^2-6y+x^2-10x+18)(y^2-12y+x^2-6x+41)=0 [-20, 20, -10, 10]}

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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.

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- The pre-image point B(-4,3) is translated to B(-1, 1). what was the translation used?
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- Point A is at #(9 ,5 )# and point B is at #(2 ,4 )#. Point A is rotated #pi # 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?
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