Question #bf75f

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Question #bf75f

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Answer 1 · 2016-06-23T17:16:31

Answering about a center and a radius of this circle.
Center is at point $O (\frac{13}{2}, - \frac{1}{2})$ $O(13/2, -1/2)$
Radius is $\frac{3}{2} \sqrt{2}$ $3/2sqrt(2)$

Explanation:

If the question is about a center and a radius of this circle, we know that the center lies right in the middle of the endpoints of a diameter. Therefore, the coordinates of a center $O (X, Y)$ $O(X,Y)$ are
$X = \frac{5 + 8}{2} = \frac{13}{2}$ $X = (5+8)/2 = 13/2$
$Y = \frac{1 + (- 2)}{2} = - \frac{1}{2}$ $Y = (1+(-2))/2 = -1/2$

The radius $R$ $R$ is a distance from a center $O (\frac{13}{2}, - \frac{1}{2})$ $O(13/2, -1/2)$ to any of two endpoints of a diameter. We'll take the point $(5, 1)$ $(5,1)$ :
$R = \sqrt{{(\frac{13}{2} - 5)}^{2} + {(- \frac{1}{2} - 1)}^{2}} = \frac{3}{2} \sqrt{2}$ $R = sqrt((13/2-5)^2+(-1/2-1)^2)=3/2sqrt(2)$

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Question #bf75f

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