A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{π}{3}$ $( pi ) /3$ radians on the circle?

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{π}{3}$ $( pi ) /3$ radians on the circle?

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Answer 1 · 2016-03-11T12:01:38

≈ 1.481

Explanation:

To calculate length of arc , require to know radius of circle. This can be found using the centre and point on circle.
Using the $distance formula$ $color(blue)" distance formula "$

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)$

where $(x_{1}, y_{1}) and (x_{2}, y_{2}) are 2 coordinate pints$ $(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate pints "$

let $(x_{1}, y_{1}) = (2, 4) and (x_{2}, y_{2}) = (1, 3)$ $(x_1,y_1)=(2,4)" and " (x_2,y_2)=(1,3)$

so radius (r) =d $= \sqrt{{(1 - 2)}^{2} + {(3 - 4)}^{2}} = \sqrt{2}$ $= sqrt((1-2)^2 + (3-4)^2) = sqrt2$

length of arc = $2πr× fraction covered$ $2pir xx " fraction covered "$

$= 2 π \times \sqrt{2} \times \frac{\frac{π}{3}}{2 π} = \sqrt{2} \times \frac{π}{3} \approx 1.481$ $= 2pixxsqrt2 xx (pi/3)/(2pi) = sqrt2 xxpi/3 ≈ 1.481$

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{π}{3}$ $( pi ) /3$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at (2,4)(2 ,4 ) and it passes through (1,3)(1 ,3 ). What is the length of an arc covering π3( pi ) /3 radians on the circle?

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 3)$ $(1 ,3 )$ . What is the length of an arc covering $\frac{π}{3}$ $( pi ) /3$ radians on the circle?