# Answer to Question #23272 in Geometry for sara

Question #23272

circle P has a diameter with endpoints at (-4,3) and (1,6). find the center of the circle.

Expert's answer

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

So the center of circle will lay down on the middle of this straight line segment. We need to find the coordinates of the point half way between (-4,3) and (1,6).

Сenter of the circle is in the middle of diameter.

Therefore the center of the circle is:

xc = (x1+x2)/2

yc = (y1+y2)/2

xc, yc - coordinates of the center

(x1, y1) and (x2, y2) - endpoints of the diameter

x = (-4 + 1)/2 = -3/2

y = (3 + 6)/2 = 9/2

Answer: (-3/2 , 9/2)

So the center of circle will lay down on the middle of this straight line segment. We need to find the coordinates of the point half way between (-4,3) and (1,6).

Сenter of the circle is in the middle of diameter.

Therefore the center of the circle is:

xc = (x1+x2)/2

yc = (y1+y2)/2

xc, yc - coordinates of the center

(x1, y1) and (x2, y2) - endpoints of the diameter

x = (-4 + 1)/2 = -3/2

y = (3 + 6)/2 = 9/2

Answer: (-3/2 , 9/2)

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