The endpoints of the diameter of a circle are at (1, 2) and (7, -6). What is the circumference of the circle, to the nearest tenth of a unit?
15.7
31.4
62.8
78.5
Please help?
Is it B? 31.4?
centre is midpoint of the given line,
centre is ( (1+7)/2 , (2-6)/2 )
= (4,-2)
radius is distance from (1,2) to (4,-2)
= √(3^2 + (-4)^2)
= √25 = 5
carry on
Didn't have to do what I did, thought I had to find the equation of your circle
Why not just find the length of the diameter, then
perimeter = πr
= 10π
which answer approximates that ?
To find the circumference of a circle, we need to know the length of its diameter. The formula to calculate the circumference of a circle is C = πd, where C is the circumference and d is the diameter.
In this case, we are given the endpoints of the diameter of the circle, (1, 2) and (7, -6). We can use the distance formula to find the length of the diameter.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length of the diameter:
d = √((7 - 1)^2 + (-6 - 2)^2)
= √((6)^2 + (-8)^2)
= √(36 + 64)
= √100
= 10
Now that we have the diameter, we can find the circumference using the formula:
C = πd
= π(10)
To get the answer to the nearest tenth, we need to substitute the value of π. Let's use the value of π as 3.14:
C = 3.14(10)
= 31.4
Therefore, the circumference of the circle, to the nearest tenth of a unit, is 31.4. So the correct answer is option B: 31.4.