The endpoints of a diameter of a circle are A (2, 1) and B (5, 5). Find the area of the circle in terms of pi?

Solution:

Given endpoints (2, 1) and (5, 5)

The diameter can be calculated as the distance between the endpoints of the diameter.

Using the distance formula,

We have diameter d= √{(x₂ - x₁)² + (y₂ - y₁)²}

Here, x₁ = 2; y₁ = 1; x₂ = 5; y₂ = 5

d = √{(5 - 2)² + (5 - 1)²}

d = √{(3)² + (4)²}

d = √{9 + 16}

d = √25 

d = 5

Diameter of the circle is 5 units

Radius of circle is 2.5 units.

Area of the circle whose radius is r is given by πr²

Area = π(2.5)² = 6.25π sq units

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The endpoints of a diameter of a circle are A (2, 1) and B (5, 5). Find the area of the circle in terms of pi?

Summary:

The endpoints of a diameter of a circle are A (2, 1) and B (5, 5), then the area of the circle in terms of pi is 6.25π sq units