Respuesta :
First end point of the diameter of a circle = (-9,-4).
Second end point of the diameter of a circle = (3,6).
Let us find length of the of the diameter of the circle by using distance formula.
We know distance formula,
[tex]d= \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2}[/tex]
We have (x1, y1) = (-9,-4) and (x2,y2) = (3,6).
Plugging values of x1,y1, x2 and y2 in above distance formula.
[tex]Distance = \sqrt{(3-(-9))^2+ (6 - (-4))^2}[/tex]
= [tex]\sqrt{(3+9)^2 +(6+4)^2} = \sqrt{(12)^2+(10)^2}[/tex]
[tex]=\sqrt{144+ 100}[/tex]
[tex]=\sqrt{244}[/tex]
Factoring out heighest perfect square from 244.
244= 4* 61.
[tex]\sqrt{244} = \sqrt{4 * 61} = \sqrt{4} * \sqrt{61}[/tex]
Square root of 4 is 2.
[tex]\sqrt{4} * \sqrt{61} = 2 \sqrt{61}[/tex]
Therefore, diameter of the circle = [tex]2\sqrt{61}[/tex]
Radius is half of diameter.
So, dividing value of diameter by 2, we get
Radius =[tex]\frac{2\sqrt{61}}{2}=\sqrt{61}[/tex]
