A circle has a center at (8,2). The point is (3,7) is on the circle. What is the area of the circle, to the nearest tenth of a square unit?
A. 22.2 square units
B. 44.4 square units
C. 157.1 square units
D.314.2 square units
HELP PLEASE, and thanks.
The circle is
(x-8)^2 + (y-2)^2 = r^2
Plug in your point (3,7) and you have
(3-8)^2 + (7-2)^2 = r^2
Now that you have r^2, you know the area is just pi r^2.
If you get stuck, come back with your work.
I think it's 157.1 square units
To find the area of a circle, you need to know its radius.
In this case, the center of the circle is given as (8,2), and a point on the circle is given as (3,7).
To find the radius, you can use the distance formula. The distance formula is:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates, the distance between the center (8,2) and the point (3,7) is:
distance = √((3 - 8)^2 + (7 - 2)^2)
= √((-5)^2 + 5^2)
= √(25 + 25)
= √50
= 5√2
Now that we have the radius, we can calculate the area of the circle. The formula for the area of a circle is:
area = π * radius^2
Using the value of the radius we found earlier, the area of the circle is:
area = π * (5√2)^2
= π * 25 * 2
= 50π
To find the answer to the nearest tenth of a square unit, we can use an approximation for the value of π. The commonly used approximation for π is 3.14.
Therefore, the approximate area of the circle is:
area ≈ 50 * 3.14
≈ 157
From the answer choices provided, the closest option to 157 is 157.1 square units (option C).