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?
A. 15.7 units
B. 31.4 units
C. 62.8 units
D. 78.5 units
I am confused. Please help me.
Well, how long is the diameter?
It is the distance between (1, 2) and (7, -6)
distance in x = 7-1 = 6
distance in y = -6 -2 = -8
so
d = sqrt [6^2 + (-8)^2 ] = sqrt (36+64) = sqrt 100 = 10
(of course we all knew it was a 3,4,5 right triangle)
so we have a circle of diameter 10 and radius 5
You do the rest. 10 pi = ?
31.4? B?
Yes, 3.14159 * 10 = 31.4 approximately
Got it! Thanks bro!
To find the circumference of a circle, you need to know its diameter or radius. In this case, you are given the endpoints of the diameter of the circle, which are (1, 2) and (7, -6).
The formula to calculate the distance between two points in a two-dimensional plane is the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, we can use the distance formula to find the length of the diameter of the circle:
diameter = √((7 - 1)^2 + (-6 - 2)^2)
= √(6^2 + (-8)^2)
= √(36 + 64)
= √100
= 10 units
Once you have the diameter of the circle, you can calculate the circumference using the formula:
circumference = π * diameter
Since you are asked to round the answer to the nearest tenth of a unit, you can use an approximation of π as 3.14.
circumference = 3.14 * 10
= 31.4 units
Therefore, the correct answer is B. 31.4 units.