What is the center of a circle if the endpoint?

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KAntoineDoix KAntoineDoix

The diameter passes through the center. Therefore, the center is the midpoint of the diameter's endpoints.

Find the coordinates of the center of the circle using the midpoint formula.

Therefore, the center of the circle is located at (2,0)

(ノ^_^)ノ

Reagan R.

asked • 02/23/18

What is the center of a circle if the endpoints of the diameter are at (-12,-7) and (3,5)

2 Answers By Expert Tutors

Andrew M. answered • 02/23/18

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

Denise' method will give the midpoint, which is the center.

However, there is a midpoint formula based on the fact that

the center of two points is the average of the x and y values

Midpoint = ((x1+x2)/2, (y1+y2)/2)

Midpoint of (-12,-7) and (3,5) is ((-12+3)/2, (-7+5)/2) = (-4.5, -1)

The center of your circle will be at the middle of the diameter, so you need to find the midpoint of the line that goes from one point to the other, (3,5) is in quadrant I, the other is in quadrant 3.

If (X, Y) is the midpoint, than for the X coordinate value X - 3 = -12 -X

For the Y coordinate value, Y - 5 = (-7 - Y)

Hint, when you solve these, the midpoint will have a negative value:)

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One way to describe the middle of a circle is to identify the centroid. This middle-point is the center of gravity, where you could balance the triangle and spin it around.

When you graph a circle, triangle, or line segment by using coordinate axes, then you can name these middle points with a pair of x- and y-coordinates. All you need to find these middles are the coordinates of some crucial other points on the respective figures.

If the endpoints of one diameter of a circle are (x1,y1) and (x2,y2), then the center of the circle has the coordinates

You probably noticed that the center of a circle is the same as the diameter's midpoint. The center of the circle separates the diameter into two equal segments called radii (plural for radius).

The figure shows a circle with a diameter whose endpoints are (7,4) and (–1,–2). The center of the circle is at (3,1). The coordinates for the center were found by using the formula for the midpoint of a segment:

You find the length of the diameter by using the distance formula:

For the circle shown, the diameter is 10 units long.

Next, you find the length of one of the radii. Either will do — they're the same length. In this example, figure the radius length from the center of the circle (3,1) to the endpoint of the diameter (7,4):

The radius is 5 units long. But, of course, you expected this answer, because by definition, the radius is half the length of the diameter.