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

1 Answer
Apr 5, 2016

circles overlap.

Explanation:

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

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

centre of B (7,5) → (7-1 , 5+1) → (6,6)

We now require to calculate the distance between the 2 centres 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)=(2,7)" and " (x_2,y_2)=(6,6)

d =sqrt((6-2)^2+(6-7)^2) = sqrt(16+1) = sqrt17 ≈ 4.123

radius of A + radius of B = 3 + 6 = 9

Since sum of radii > distance between centres, circles overlap.