A circle's center is at #(2 ,4 )# and it passes through #(1 ,3 )#. What is the length of an arc covering #( pi ) /3 # radians on the circle?
1 Answer
Mar 11, 2016
≈ 1.481
Explanation:
To calculate length of arc , require to know radius of circle. This can be found using the centre and point on circle.
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 pints "# let
#(x_1,y_1)=(2,4)" and " (x_2,y_2)=(1,3)# so radius (r) =d
#= sqrt((1-2)^2 + (3-4)^2) = sqrt2# length of arc =
#2pir xx " fraction covered "#
# = 2pixxsqrt2 xx (pi/3)/(2pi) = sqrt2 xxpi/3 ≈ 1.481#