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. 15.7units
b. 31.4 units
c. 62.8 units
d. 78.5 units
C
B
C
B
C
D
B
C
A
C
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use the distance formula to find the length of the diameter.
Then, C = πd
What is the center of the circle that has a diameter whose endpoints are (6, -4) and (18, 10)?
To find the circumference of a circle, we can use the formula:
C = π × d
where C is the circumference and d is the diameter of the circle.
First, let's find the length of the diameter using the given endpoints (1,2) and (7,-6).
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
For our given points (1, 2) and (7, -6), the formula becomes:
d = √((7 - 1)² + (-6 - 2)²)
= √(6² + (-8)²)
= √(36 + 64)
= √100
= 10
So, the diameter of the circle is 10 units.
Now, substituting this value of d into the circumference formula, we have:
C = π × 10
≈ 31.4 units
Therefore, the circumference of the circle to the nearest tenth of a unit is approximately 31.4 units.
So, the correct answer is (b) 31.4 units.
Use distance formula or Pythagorean theorem.
Pythagorean-
6^2+8^2= radius^2
100= radius^2
10= radius
radius= r
Use circumference formula.
C=2pir
C=2pi10
C=62.83
C