Question

A circle is graphed on a coordinate grid. Its center is at (3, 4), and the circle passes through point (3, 1). What is the approximate area, in square units, of the circle?

Answer 1

To find the area of the circle, we need to know its radius. The radius is the distance from the center of the circle to any point on its circumference. In this case, the circle passes through the point (3, 1), which means the distance from the center to that point is the radius.

Step-by-step explanation:

To find the area of the circle, we need to know its radius. The radius is the distance from the center of the circle to any point on its circumference. In this case, the circle passes through the point (3, 1), which means the distance from the center to that point is the radius.

The formula to find the distance between two points is sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the given values, we get sqrt((3 - 3)^2 + (1 - 4)^2) = sqrt(0 + 9) = sqrt(9) = 3.

Now that we know the radius is 3, we can calculate the area of the circle using the formula A = πr^2. Plugging in the value of r, we get A = π(3)^2 = 9π. Approximating π as 3.14, the approximate area of the circle is 9 * 3.14 = 28.26 square units.