# Circle A has a radius of #5 # and a center of #(2 ,7 )#. Circle B has a radius of #1 # 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?

no overlap , min. distance ≈ 0.082 units

What we have to do here is to 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

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

(6 ,1) → (6+2 ,1+7) → (8 ,8) is the new centre of circle B

Here the 2 points are (2 ,7) and (8 ,8) the centres of the circles.

sum of radii = radius of A + radius of B = 5 + 1 = 6

Since sum of radii < d , then no overlap

min. distance between points = d - sum of radii

= 6.082 - 6 = 0.082 units (3 decimal paces) graph{(y^2-16y+x^2-16x+127)(y^2-14y+x^2-4x+28)=0 [-52, 52, -26.1, 25.9]}

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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 ,1 )#. Circle B has a radius of #1 # and a center at #(3 ,2 )#. If circle B is translated by #<-2 ,6 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A triangle has corners at #(3, 9 )#, ( 6, -5)#, and #( 4, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- 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?
- Points A and B are at #(6 ,1 )# and #(3 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- A triangle has corners at #(2, 7 )#, #( 6, 3 )#, and #( 2 , 5 )#. If the triangle is dilated by # 2 x# around #(2, 5)#, what will the new coordinates of its corners be?

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