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inessss [21]
3 years ago
11

Please and thank you (=

Mathematics
1 answer:
balu736 [363]3 years ago
7 0
So hmm check the picture below

the diameter has those endpoints, recall the radius is half the diameter

the diameter length is \bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 0}}\quad ,&{{ 4}})\quad 
%  (c,d)
&({{ 6}}\quad ,&{{ -4}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}

the radius is  half that

and the center will be half-way on that segment, namely, the MidPoint

so the center will be at \bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 0}}\quad ,&{{ 4}})\quad 
%  (c,d)
&({{ 6}}\quad ,&{{ -4}})
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)\\\\
-----------------------------\\\\
h=\cfrac{{{ x_2}} + {{ x_1}}}{2}\qquad \qquad k=\cfrac{{{ y_2}} + {{ y_1}}}{2}

so plug those three\bf (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad center\ ({{ h}},{{ k}})\qquad
radius={{ r}} at  

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