Question

Circle A has a radius of `4` and a center of `(6 ,1 )`. Circle B has a radius of `1` and a center of `(4 ,5 )`. If circle B is translated by `<-3 ,2 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

no overlap , d ≈ 2.81

Explanation:

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

Under a translation of `((-3),(2))`

centre B (4,5) → (4-3 , 5+2) → (1 , 7)

Calculate the distance between the centres of A and B using the `color(blue)" distance formula "`

`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "`

let `(x_1,y_1)=(6,1)" and " (x_2,y_2)=(1,7)`

d `=sqrt((1-6)^2 + (7-1)^2) = sqrt(25+36) = sqrt61 ≈ 7.81`

radius of A + radius of B = 4 + 1 = 5

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

and distance between them = 7.81 - 5 = 2.81