Question

Circle A has a radius of `1` and a center at `(2 ,4 )`. Circle B has a radius of `3` and a center at `(6 ,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?

Answer 1

no overlap , d ≈ 1.099

Explanation:

A translation does not change the shape of a figure, only it's position.

Under a translation of `((-3),(4))`

centre of B(6 , 5) → (6 -3 ,5 + 4) → (3 , 9)

Now, require to calculate the distance between the centres of A and B using the `color(blue)" distance formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "`

let `(x_1,y_1)=(2,4)" and " (x_2,y_2)=(3,9)`

d`= sqrt((3-2)^2 + (9-4)^2) = sqrt(1+25) = sqrt26 ≈ 5.099`

now radius of A + radius of B = 1 + 3 = 4

Since sum of radii < distance between centres , no overlap.

and distance (d) between circles = 5.099 - 4 = 1.099