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.

the length of the diameter is

√((7-1)^2+(-6-2)^2) = 10

Now you can find the circumference, right?

31.4

To find the circumference of a circle, we need to know its radius. In this case, we can find the radius by finding the distance between the two endpoints of the diameter.

Using the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Let's plug in the coordinates:

Distance = √((7 - 1)^2 + (-6 - 2)^2)
= √(6^2 + (-8)^2)
= √(36 + 64)
= √100
= 10

Therefore, the distance between the two endpoints is 10 units.

Now, we know that the diameter of the circle is 10 units. The formula to find the circumference of a circle is:

Circumference = π * diameter

Using π as approximately 3.14:

Circumference = 3.14 * 10
= 31.4

So, the circumference of the circle is approximately 31.4 units, to the nearest tenth of a unit.

To find the circumference of a circle, you need to know its radius or diameter. In this case, we are given the endpoints of the diameter of the circle, which are (1,2) and (7,-6).

To find the distance between two points, we can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the distance between the two endpoints first:

Distance = √((7 - 1)^2 + (-6 - 2)^2)
= √(6^2 + (-8)^2)
= √(36 + 64)
= √100
= 10

Thus, the diameter of the circle is 10 units.

The formula to calculate the circumference of a circle is:

Circumference = π × Diameter

Since we know the diameter is 10 units, we can substitute into the formula:

Circumference = π × 10

Now, to find the value of π to the nearest tenth, we can use the approximation 3.14.

Circumference = 3.14 × 10
= 31.4

Therefore, the circumference of the circle, to the nearest tenth of a unit, is approximately 31.4 units.