A circle has a center at (1 ,3 ) and passes through (2 ,1 ). What is the length of an arc covering pi /4 radians on the circle?

1 Answer
Jim G.
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 "

d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

where (x_1,y_1)" and "(x_2,y_2)" are 2 coordinate points "

let (x_1,y_1)= (1,3)" and "(x_2,y_2)=(2,1)

radius (r ) =sqrt((2-1)^2 + (1-3)^2) = sqrt5

length of arc = 2pir xx "fraction of circle covered "

= cancel(2pi)xxsqrt5 xx (pi/4)/cancel(2pi) = sqrt5xxpi/4 ≈ 1.756

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