A circle's center is at #(5 ,4 )# and it passes through #(1 ,7 )#. What is the length of an arc covering #(5pi ) /8 # radians on the circle?

Question

How many degrees does the hour hand of a clock turn in 5 minutes?
A circle has a center at #(3 ,1 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,6 )# and passes through #(2 ,1 )#. What is the length...
A circle has a center at #(7 ,3 )# and passes through #(2 ,7 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,4 )#. What is the length of...
A circle has a center at #(1 ,3 )# and passes through #(2 ,1 )#. What is the length of...
A circle has a center at #(1 ,2 )# and passes through #(4 ,7 )#. What is the length of...

1656 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-25T10:10:14

The arc length is #L=(25pi)/8#

To find the arc length we have to find circle's radius. To calculate it we use the given points. The radius is the distance between given points:

#r=sqrt((5-1)^2+(4-7)^2)=sqrt(4^2+(-3)^2)=sqrt(16+9)=5#

Now we can calculate the arc length:

#L=2pir*alpha/(2pi)=r*alpha=(5pi)/8*5=(25pi)/8#