A circle has a center at (1 ,3 )(1,3) and passes through (2 ,1 )(2,1). What is the length of an arc covering pi /4 π4 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 " distance formula
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)d=√(x2−x1)2+(y2−y1)2 where
(x_1,y_1)" and "(x_2,y_2)" are 2 coordinate points "(x1,y1) and (x2,y2) are 2 coordinate points let
(x_1,y_1)= (1,3)" and "(x_2,y_2)=(2,1) (x1,y1)=(1,3) and (x2,y2)=(2,1) radius (r )
=sqrt((2-1)^2 + (1-3)^2) = sqrt5 =√(2−1)2+(1−3)2=√5 length of arc =
2pir xx "fraction of circle covered "2πr×fraction of circle covered
= cancel(2pi)xxsqrt5 xx (pi/4)/cancel(2pi) = sqrt5xxpi/4 ≈ 1.756
