the endpoints of the diameter of a circle are at (1,2) and (7, -6). what is the circumference of the circle, no the nearest tenth of a unit?
15.7
31.4
62.8
78.5
I was thinking B? i want to check.
You are correct
To find the circumference of a circle, you first need to calculate the length of the diameter.
The formula for finding the distance between two points in a coordinate plane is the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two endpoints of the diameter are (1,2) and (7,-6). Let's label them as (x1, y1) = (1,2) and (x2, y2) = (7,-6).
Substituting these values into the distance formula, we get:
d = √((7 - 1)^2 + (-6 - 2)^2)
Simplifying further:
d = √(6^2 + (-8)^2)
d = √(36 + 64)
d = √100
d = 10
So, the length of the diameter is 10 units.
The formula for finding the circumference of a circle is:
C = πd
where C is the circumference, d is the diameter, and π (pi) is approximately 3.14159.
Substituting the value of the diameter, we get:
C = 3.14159 * 10
C ≈ 31.4159
Rounding to the nearest tenth, the circumference is approximately 31.4 units.
Therefore, the correct option is B: 31.4.