Question

The center point of a circle has the coordinates (3, 2). There is a point on the circle that has the coordinates (−2.2, 2). What is the length of the diameter of the circle?(1 point)

Answer 1

To find the diameter of the circle, we first need to calculate the radius. The radius is the distance from the center of the circle to a point on the circle.

The center of the circle is at the coordinates \((3, 2)\) and a point on the circle is at the coordinates \((-2.2, 2)\).

We can use the distance formula to find the radius. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates of the center and the point on the circle into the formula:

- \((x_1, y_1) = (3, 2)\)
- \((x_2, y_2) = (-2.2, 2)\)

Now substituting into the distance formula:

\[
d = \sqrt{((-2.2 - 3)^2) + (2 - 2)^2}
\]
\[
= \sqrt{((-5.2)^2) + 0^2}
\]
\[
= \sqrt{27.04}
\]
\[
= 5.2
\]

The radius of the circle is \(5.2\). The diameter \(D\) of the circle is twice the radius:

\[
D = 2 \times \text{radius} = 2 \times 5.2 = 10.4
\]

Therefore, the length of the diameter of the circle is \(10.4\).