# A circle has a center at #(1 ,3 )# and passes through #(2 ,1 )#. What is the length of an arc covering #pi /4 # radians on the circle?

##### 1 Answer

Mar 11, 2016

≈ 1.756 units

#### Explanation:

To calculate length of arc , the radius is required. This can be found using the 2 points given and 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)= (1,3)" and "(x_2,y_2)=(2,1) # radius (r )

#=sqrt((2-1)^2 + (1-3)^2) = sqrt5 # length of arc =

#2pir xx "fraction of circle covered "#

# = cancel(2pi)xxsqrt5 xx (pi/4)/cancel(2pi) = sqrt5xxpi/4 ≈ 1.756#