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"
