A circle has a center at (8, 2). The point (3, 7) is on the circle. What is the area of the circle to the nearest tenth of a square unit?
you just need to find r. You have a point on the circle, which is r units away from the center. Thus,
(3-8)^2 + (7-2)^2 = r^2
now you can easily find the area.
A(-3,2),B(1,-2),(1,3)
To find the area of the circle, we'll need to know the radius. The distance between the center of the circle (8, 2) and the point on the circle (3, 7) is the radius.
Using the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Let's plug in the values:
Distance = √((3 - 8)² + (7 - 2)²)
= √((-5)² + 5²)
= √(25 + 25)
= √50
≈ 7.1
So, the radius of the circle is approximately 7.1 units.
Now, we can use the formula for the area of a circle:
Area = π * radius²
Plugging in the value of the radius:
Area ≈ 3.14 * 7.1²
≈ 3.14 * 50.41
≈ 158.29
Therefore, the area of the circle, to the nearest tenth of a square unit, is approximately 158.3 square units.