Question

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

Answer 1

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