A circle has a center at : Left-parenthesis 8 comma 2 right-parenthesis. The point Left-parenthesis 3 comma 7 right-parenthesis is on the circle. What is the area of the circle, to the nearest tenth of a square unit?
(1 point)
Responses
22.2 square units
22.2 square units
44.4 square unit
44.4 square unit
157.1 square units
157.1 square units
314.2 square units
To find the area of a circle, we need to know the radius. The distance from the center of the circle to a point on the circle is the radius. Using the distance formula, we can find the distance between the center (8,2) and the point (3,7):
d = sqrt((x2-x1)^2 + (y2-y1)^2)
d = sqrt((3-8)^2 + (7-2)^2)
d = sqrt((-5)^2 + (5)^2)
d = sqrt(25 + 25)
d = sqrt(50)
d = 7.1 (rounded to the nearest tenth)
The radius of the circle is 7.1. Now, we can use the formula for the area of a circle:
A = πr^2
A = π(7.1)^2
A = 157.1 square units
Therefore, the area of the circle is approximately 157.1 square units (to the nearest tenth). So, the correct answer is:
157.1 square units
To find the area of the circle, we need to find the radius first.
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)
distance = √((3 - 8)^2 + (7 - 2)^2)
distance = √((-5)^2 + 5^2)
distance = √(25 + 25)
distance = √50
distance ≈ 7.1
Now that we have the radius, we can use the formula for the area of a circle.
Area = π * r^2
Area = 3.14 * 7.1^2
Area ≈ 157.1 square units
Therefore, the area of the circle, to the nearest tenth of a square unit, is 157.1 square units.