The endpoints of a diameter on a circle are a(2,1)and B(5,5). Find the area of the circle in terms of 3.14.
To find the area of the circle, we need to determine the radius first. Since we are given the endpoints of a diameter, we can use the distance formula to calculate the length of the diameter.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Here, (x1, y1) = (2, 1) and (x2, y2) = (5, 5). Plugging in the values, we have:
d = √((5 - 2)^2 + (5 - 1)^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5
Now, we know that the diameter is 5 units. Since the radius of a circle is half its diameter, the radius would be 5/2 = 2.5 units.
The formula for the area of a circle is:
A = πr^2
Plugging in the value of the radius, we get:
A = 3.14 * (2.5)^2
= 3.14 * 6.25
= 19.625
Hence, the area of the circle, in terms of 3.14, is 19.625 square units.
the diameter of the circle is the distance between the points. That distance is 5.
So, now you know the radius is 5/2, and you can take it from there.