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)
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.