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Dmitrij [34]
3 years ago
12

the circle shown below is centered at the origin and contains the point (-4,-2). Which of the following is closest to the length

of the diameter of the circle?
Mathematics
2 answers:
aniked [119]3 years ago
8 0
We know the circle has its center at the origin, 0,0, and the point -4,-2 is on the circle, is just the distance from the center to a point on it, thus

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 0}}\quad ,&{{ 0}})\quad 
%  (c,d)
&({{ -4}}\quad ,&{{ -2}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
r=\sqrt{(-4-0)^2+(-2-0)^2}\implies r=\sqrt{(-4)^2+(-2)^2}
\\\\\\
r=\sqrt{16+4}\implies r=\sqrt{20}\implies r=\sqrt{4\cdot 5}\implies r=\sqrt{2^2\cdot 5}
\\\\\\
r=2\sqrt{5}
MrMuchimi3 years ago
7 0

Answer:

Diameter=2\sqrt{20}

Step-by-step explanation:

In order to solve this you first have to calculate the radius, which is the distance from the center to any point in the circumference, to calculate this we do a trangle rectangle:

c^2= a^2+b^2

c^2=(0-(-4))^2+(0-(-2)^2

c^2=20

c=\sqrt{20}

So the diameter is two ratios put togheter, so it would be 2r= 2\sqrt{20}

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