What is the area of the circle if the diameter has endpoints (2,7) and (-4, -1).

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.