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

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