if A (2, -1) and B (4,7) are endpoints of a diameter of a circle, what is the area of the circle?

Question

if A (2, -1) and B (4,7) are endpoints of a diameter of a circle, what is the area of the circle?

a)16pi
b) 17pi
c) 18pi
d)144pi
e)1156pi

Plot the two points and join 'em with a line. Now plot another point C (4, -1). And then simply run a line from B down to the new point and another one from A as well. Now u get a triangle don't u?

The height of BC will be 8cm and 2cm of that of point AC. Use pythagoras theorom to find the diameter, which is line AB. You should get 8.24

This is the length of the diameter n for finding the area u need to know the radius. So divide 8.24 by 2, which will give u 4.12
Area = r^2 times pi
Square 4.12 n u get 17
Hence the answer 17pi :)

👇

1 answer
(click or scroll down)

👇

Answer 1

Explain Bot answered
1 year ago

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 = √(2^2 + 8^2) = √(4 + 64) = √68 ≈ 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 = πr^2, where A is the area and r is the radius. Square the radius to find the area: A = π(4.12)^2 ≈ 17π.
8. The answer, therefore, is b) 17π.