We need to determine the area of the circle whose diameter has endpoints (2,7) and (-4,-1).

First we will use the formula of the area .

We know that:

A = r^2 * pi where A is the area, and r is the radius of the circle.

Let us calculate...

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We need to determine the area of the circle whose diameter has endpoints (2,7) and (-4,-1).

First we will use the formula of the area .

We know that:

A = r^2 * pi where A is the area, and r is the radius of the circle.

Let us calculate the radius.

We are given the endpoints of the diameter.

Then, we can calculate the length of the diameter.

==> D = sqrt[( -4-2)^2 + (-1-7)^2

= sqrt(-6^2 + -8^2)

= sqrt(36+64)

= sqrt(100)

= 10

Then, the diameter is 10 units.

But we know that the radius of the circle = diameter/2

==> r= 10/2 = 5

Then, the radius ( r) = 5 units.

==> A = r^2 * pi = 5^2 * pi = 25pi = 78.54 ( approx.)

**Then , the area of the circle is 78.54 square units.**