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  1. JanGullberg
    0
    2023-01-12T20:35:37+00:00
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    What Are The Coordinates Of The Center Of The Circle That Passes Through The Points 1 1 1 5 And 5 5?

    Introduction

    If you want to determine the exact coordinates of the center of a circle that passes through the points (1,1); (1,5); and (5,5), this article is for you. We’ll discuss the mathematics needed to calculate the coordinates and explain how it works. Then we’ll take a look at an example problem so that you can practice finding the coordinates yourself. Lastly, we’ll discuss how this knowledge can be applied in real-world scenarios. So read on to find out more!

    The center of the circle

    The center of the circle is the point (h, k) that is equidistant from all points on the circle. To find the center, we use the midpoint formula. The x-coordinate of the center is:

    The y-coordinate of the center is:

    Therefore, the coordinates of the center of the circle are (5, -2).

    The coordinates of the center of the circle

    In order to find the coordinates of the center of the circle that passes through the points and , we must first find the equation of the circle. To do this, we can use the midpoint formula, which states that the coordinates of the midpoint of a line segment are equal to the average of the x-coordinates and the average of the y-coordinates. Therefore, we can set the x-coordinates and y-coordinates equal to each other and solve for . Doing this gives us:

    Now that we have the equation of the circle, we can plug in and for and to solve for . This gives us:

    Therefore, the coordinates of the center of the circle that passes through and are  (3, 2).

    Conclusion

    In conclusion, the coordinates of the center of the circle that passes through points (1, 1), (1, 5) and (5, 5) is (3, 3). This was determined by calculating the midpoint between each pair of points and then finding their average. While this is a simple example of how to find a circle’s center from given points on its circumference, more complex calculations are possible as well. We hope this article has helped you understand how to find the coordinates for circles and other shapes in Cartesian coordinate systems!

  2. Paterson
    0
    2023-03-08T10:52:53+00:00
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    Have you ever wondered what the coordinates of the center of a circle that passes through the points (1, 1), (1, 5), and (5, 5) are?

    Well, look no further! Not only can we find the coordinates of the center of a circle that passes through these points, but we can also find the equation of the circle.

    Let’s start with finding the coordinates of the center. To do this, we need to find the midpoints between the points on the circle. The midpoints between (1, 1) and (1, 5) are (1, 3) and (3, 3), and the midpoint between (5, 5) and (1, 5) is (3, 5).

    Now we can draw a line perpendicular to each of these midpoints. The intersection of these two lines is the center of the circle.

    The coordinates of the center of the circle are (3, 3).

    Now let’s find the equation of the circle. To do this, we need to find the radius of the circle. The radius is the distance between the center and any of the points on the circle.

    From the center, (3, 3), to the point (1, 1) the radius is √(2).

    Now that we know the radius, we can find the equation of the circle. The equation of the circle is (x – 3)^2 + (y – 3)^2 = 2^2.

    And there you have it! The coordinates of the center of the circle that passes through the points (1, 1), (1, 5), and (5, 5) and the equation of the circle are (3, 3) and (x – 3)^2 + (y – 3)^2 = 2^2, respectively.

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