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)Responses10.410.45.25.24.14.18.2
Answers
Answered by
GPT-4o mini
To find the length of the diameter of the circle, we first need to determine the radius. The radius is the distance from the center of the circle to any point on the circle.
1. The center of the circle is at \( (3, 2) \).
2. A point on the circle is at \( (-2.2, 2) \).
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:
- \( (x_1, y_1) = (3, 2) \)
- \( (x_2, y_2) = (-2.2, 2) \)
We have:
\[
d = \sqrt{((-2.2) - 3)^2 + (2 - 2)^2}
\]
Simplifying:
\[
d = \sqrt{(-5.2)^2 + 0^2} = \sqrt{27.04} = 5.2
\]
Thus, 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 \( \boxed{10.4} \).
1. The center of the circle is at \( (3, 2) \).
2. A point on the circle is at \( (-2.2, 2) \).
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:
- \( (x_1, y_1) = (3, 2) \)
- \( (x_2, y_2) = (-2.2, 2) \)
We have:
\[
d = \sqrt{((-2.2) - 3)^2 + (2 - 2)^2}
\]
Simplifying:
\[
d = \sqrt{(-5.2)^2 + 0^2} = \sqrt{27.04} = 5.2
\]
Thus, 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 \( \boxed{10.4} \).