A circle has a center at #(7 ,2 )# and passes through #(1 ,1 )#. What is the length of an arc covering #(3pi ) /4 # radians on the circle?
1 Answer
Mar 2, 2018
Explanation:
#"the length (l) of the arc is found using"#
#•color(white)(x)l="circumference "xx" fraction of circle"#
#color(white)(xxx)=2pirxx((3pi)/4)/(2pi)#
#"for this calculation we require to find r the radius"#
#"the distance from the centre to the point on the "#
#"circumference is the radius"#
#"to calculate the radius r use the "color(blue)"distance formula"#
#•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#"let "(x_1,y_1)=(1,1)" and "(x_2,y_2)=(7,2)#
#rArrr=sqrt((7-1)^2+(2-1)^2)=sqrt(36+1)=sqrt37#
#rArrl=cancel(2pi)xxsqrt37xx((3pi)/4)/cancel(2pi)#
#color(white)(rArrl)=(sqrt37xx3pi)/4~~14.33" units"#
