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

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

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Answer 1 · 2018-04-21T17:41:43

$\frac{3 π \sqrt{5}}{4}$ $color(blue)((3pisqrt(5))/4)$

Explanation:

If the centre of the circle has coordinates $(3, 2)$ $(3,2)$ and the point $(1, 1)$ $(1,1)$ lies on the circumference, then the length of the radius is the distance between these points. This can be found using the distance formula.

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

$d = \sqrt{{(3 - 1)}^{2} + {(2 - 1)}^{2}} = \sqrt{5}$ $d=sqrt((3-1)^2+(2-1)^2)=sqrt(5)$

If we rotate the terminal side $\frac{3 π}{4}$ $(3pi)/4$ to form a sector, then the angle subtended by the arc at the centre will also be $\frac{3 π}{4}$ $(3pi)/4$

Arc length is given by:

$r θ$ $rtheta$

$:.$

$sqrt(5)((3pi)/4)=(3pisqrt(5))/4$

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

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Explanation:

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A circle has a center at (3 ,2 )(3,2)(3 ,2 ) and passes through (1 ,1 )(1,1)(1 ,1 ). What is the length of an arc covering (3pi ) /4 3π4(3pi ) /4 radians on the circle?

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