Question

A circle has a center at `(7 ,9 )` and passes through `(1 ,3 )`. What is the length of an arc covering `pi /4` radians on the circle?

Answer 1

`pi/4=45^o and (45^o)/(360^o)=1/8 " of the circumference"`

Circumference `=2pir` so, the length of the arc is `(1/8)(2pir)`

Explanation:

The radius is the distance between the center and the point on the circle:

Using the distance formula ...

radius `=sqrt[(7-1)^2+(9-3)^2]=6sqrt2`

length of the arc is `=(1/8)(2pir)=(1/8)[2pi(6sqrt2)]=1.5pisqrt2`

hope that helped