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Sagot :
Given:
A circle has diameter endpoints at (-1, 1) and (14, 18)
The center is the mid-point of the diameter
so, we will find the midpoint using the given points as follows:
[tex]C=\frac{(-1,1)+(14,18)}{2}=\frac{(-1+14,1+18)}{2}=\frac{(13,19)}{2}=(\frac{13}{2},\frac{19}{2})[/tex]So, the coordinates of the center = C = (13/2, 19/2)
The diameter is the distance between the given points
We will find the distance using the following formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute with the given points
so,
[tex]d=\sqrt[]{(14+1)^2+(18-1)^2}=\sqrt[]{15^2+17^2}=\sqrt[]{514}\approx22.67[/tex]The radius of the circle = 0.5 * d
so, the radius = 0.5 * 22.67 = 11.335
So, the answer will be:
[tex]\begin{gathered} center=(\frac{13}{2},\frac{19}{2}) \\ radius=11.335 \end{gathered}[/tex]
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