A circle's center is at #(7 ,5 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?
1 Answer
Mar 8, 2016
≈ 19.83
Explanation:
To calculate the length of arc , require to know radius of circle.
This can be found 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 coord points "# The 2 points here are the centre and the point it passes through. This distance is the radius of the circle.
let
#(x_1,y_1)=(7,5)" and " (x_2,y_2)=(5,8) # hence r
#=sqrt((5-7)^2+(8-5)^2)=sqrt(4+9)=sqrt13# arc length = circumference
#xx " fraction of circle covered "# arc length =
#2pirxx((7pi)/4)/(2pi) = cancel((2pi)r)xx((7pi)/4)/cancel(2pi) =rxx(7pi)/4#
#rArr" arc length " = sqrt13xx(7pi)/4 ≈ 19.83 #
