Question

Circle A has a radius of `2` and a center of `(6 ,2 )`. Circle B has a radius of `3` and a center of `(5 ,7 )`. If circle B is translated by `<-1 ,2 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

no overlap , d ≈ 2.28

Explanation:

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

Under a translation of `((-1),(2))`

Centre of B (5 , 7) → (5-1 , 7 + 2 ) → (4 , 9)

Now require to 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)=(6,2)" and " (x_2,y_2)=(4,9)`

d `= sqrt((4-6)^2 + (9-2)^2) = sqrt(4 + 49) = sqrt53 ≈ 7.28`

now, radius of A + radius of B = 2 + 3 = 5

Since sum of radii < distance between centres , no overlap

and distance between circles (d) = 7.28 - 5 = 2.28