## To find the area of a circle given the coordinates of its endpoints, you can follow these steps:

1. Plot the two given points, A (2, -1) and B (4, 7), on a graph.

2. Join the two points with a straight line to create a diameter of the circle.

3. Choose a third point, C, on the graph aligned with point B but with the same x-coordinate as point A. In this case, C(4, -1).

4. Draw lines from points A and C to point B. This creates a triangle, ABC, with side lengths AB, AC, and BC.

5. Use the Pythagorean theorem to find the length of the diameter AB. The formula is c^2 = a^2 + b^2, where c is the hypotenuse (AB) and a and b are the other two sides (AC and BC). In this case, AC = 2 and BC = 8, therefore AB = âˆš(2^2 + 8^2) = âˆš(4 + 64) = âˆš68 â‰ˆ 8.24.

6. The diameter AB is equal to twice the radius of the circle. Divide the length of AB by 2 to find the radius. In this case, the radius = 8.24 / 2 = 4.12.

7. The formula for the area of a circle is A = Ï€r^2, where A is the area and r is the radius. Square the radius to find the area: A = Ï€(4.12)^2 â‰ˆ 17Ï€.

8. The answer, therefore, is b) 17Ï€.