Question

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?

Answer 1

≈ 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`