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

Answer:

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

Step-by-step 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:

$M = (\frac{x_{1}+ x_{2} }{2} ,\frac{y_{1}+ y_{2} }{2} )$

$M = (\frac{2 + (-8) }{2} ,\frac{5 + 29 }{2} ) = (\frac{-6}{2} ,\frac{34}{2} ) = (-3, 17)$

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:

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

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

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

$d = \sqrt{100 + 576}$

$d = \sqrt{676} = 26$

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