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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

The diameter of a circle has the endpoints of (2,5) and (-8, 29). Find the center-example-1
User Mikewaters
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1 Answer

5 votes

Answer:

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.

User Nwalke
by
6.2k points
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