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 #