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Find the diameter of this circle.

A. [tex]2\sqrt{10}[/tex]
B. [tex]4\sqrt{10}[/tex]
C. 8
D. [tex]2\sqrt{34}[/tex]

Find The Diameter Of This Circle A Tex2sqrt10tex B Tex4sqrt10tex C 8 D Tex2sqrt34tex class=

Sagot :

Answer:

A

Step-by-step explanation:

From looking at the graph, you can see that the center point of the circle is at (5, -3), so to figure out the diameter, you need to find the distance of that line ( y = - 3 ) that the circle is on. The diameter is about 6 point something which in the square root form can be represented by √36.

After knowing the diameter is about 6, choice C can be eliminated.

2√10 = √40

4√10 = √160

2√34 = √136

After expanding the square root, we can know that the closest option is A.

Check the picture below.

so we know the circle has that center and passes through (2 , -2), let's find its radius, keeping in mind that diameter = 2 * radius.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~5 - 2~~)^2 + (~~-3 - (-2)~~)^2} \implies r=\sqrt{(5 -2)^2 + (-3 +2)^2} \\\\\\ r=\sqrt{( 3 )^2 + ( -1 )^2} \implies r=\sqrt{ 9 + 1 } \implies r=\sqrt{ 10 }~\hfill \underset{diameter}{\stackrel{(2)(r)}{2\sqrt{10}}}[/tex]

View image jdoe0001
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