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.
