Question

The diameter of a circle has the endpoints of (2,5) and (-8, 29).

Find the center and radius of the circle.

A) Center: (5,12)
Radius: 13
B) Center: (-5,17)
Radius: 26
C) Center: (-3,17)
Radius: 612
D) Center: (-3,17)
Radius: 13

Answer 1

Correct answer: D) Center: (-3, 17), Radius: 13

Explanation:

Given the diameter of a circle with endpoints: (2, 5) (-8, 29):

Let
`(x_(1), y_(1))` = (2, 5)

`(x_(2), y_(2))` = (-8, 29)

To find the center of the circle, we can use the Midpoint formula:

`M = ((x_(1)+ x_(2) )/(2) ,(y_(1)+ y_(2) )/(2) )`

`M = ((2 + (-8) )/(2) ,(5 + 29 )/(2) ) = ((-6)/(2) ,(34)/(2) ) = (-3, 17)`

Therefore, the center of the circle is (-3, 17).

We can use the distance formula to find the actual distance between these endpoints, and to help determine the radius of the circle.

The distance formula is:

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)}`

`d = \sqrt{(-8 - 2)^(2) + (29 - 5)^(2)}`

`d = \sqrt{(-10)^(2) + (24)^(2)}`

`d = √(100 + 576)`

`d = √(676) = 26`

Therefore, the diamater of the circle is 26, which means that the radius is 13.