Problem Analysis:
The image shows a circle centered at the origin of a Cartesian coordinate system. The task is likely to determine the equation of the circle or some related property, such as its radius or center.
Step-by-Step Solution:
1.
Identify the Center of the Circle:
- The circle is centered at the origin of the coordinate system. The origin is the point where the x-axis and y-axis intersect, which is \((0, 0)\).
2.
Determine the Radius of the Circle:
- To find the radius, we need to measure the distance from the center of the circle to any point on its circumference.
- From the grid, we can see that the circle passes through the points \((3, 0)\), \((-3, 0)\), \((0, 3)\), and \((0, -3)\).
- The distance from the center \((0, 0)\) to any of these points is 3 units. Therefore, the radius \(r\) of the circle is 3.
3.
Write the Equation of the Circle:
- The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
- Here, the center \((h, k)\) is \((0, 0)\) and the radius \(r\) is 3. Substituting these values into the equation, we get:
\[
(x - 0)^2 + (y - 0)^2 = 3^2
\]
Simplifying this, we have:
\[
x^2 + y^2 = 9
\]
Final Answer:
The equation of the circle is:
\[
\boxed{x^2 + y^2 = 9}
\]
This equation represents a circle centered at the origin with a radius of 3.
Parent Tip: Review the logic above to help your child master the concept of circles in the coordinate plane worksheet answers.
