A circle has a center at $(7, 9)$ $(7 ,9 )$ 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 $(7, 9)$ $(7 ,9 )$ 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 · 2016-02-03T12:42:29

$\frac{15 π}{2}$ $(15pi)/2$

Explanation:

First thing to do is to find the length of the radius. The line segment joining the center of the circle to any point on the circle constitutes a radius.

Therefore, the line segment joining $(7, 9)$ $(7,9)$ and $(1, 1)$ $(1,1)$ is a radius. To find its length, you can use Pythagoras Theorem.

$r = \sqrt{{(7 - 1)}^{2} + {(9 - 1)}^{2}} = 10$ $r = sqrt{(7 - 1)^2 + (9 - 1)^2} = 10$

Next, you should know that an arc subtending an angle of $θ$ $theta$ in radians, has arc length, s, given by $s = r θ$ $s = r theta$ .

$s = (10) \cdot (\frac{3 π}{4}) = \frac{15 π}{2}$ $s = (10)*((3pi)/4) = (15pi)/2$

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A circle has a center at $(7, 9)$ $(7 ,9 )$ 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 $(7, 9)$ $(7 ,9 )$ 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?