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

Question

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

1 Answer

Impact of this question

3073 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-23T10:53:45

I found $28.3$ $28.3$ units but have a look at my method.

Explanation:

I would first find the radius $r$ $r$ as the distance between the center and your given point:
$r = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}} = \sqrt{{(4 - 1)}^{2} + {(2 - 2)}^{2}} = \sqrt{3^{2} + 0^{2}} = 3$ $r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)=sqrt((4-1)^2+(2-2)^2)=sqrt(3^2+0^2)=3$

Then I would consider that the length $s$ $s$ of an arc of angle $θ$ $theta$ (in radians) will be:
$s = r \cdot θ$ $s=r*theta$
so that:
$s = 3 \cdot \frac{π}{4} = \frac{3}{4} \cdot 3.14 = 28.27 \approx 28.3$ $s=3*pi/4=3/4*3.14=28.27~~28.3$ units

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A circle has a center at (1 ,2 )(1,2)(1 ,2 ) and passes through (4 ,2 )(4,2)(4 ,2 ). What is the length of an arc covering pi /4 π4pi /4 radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

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