Question

A circle has a center at (−4,−1) and a point at (2,−1.5). What is the length of the diameter of the circle? Round your answer to the nearest tenth.(1 point)d=

Answer 1

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

The center of the circle is at \((-4, -1)\) and a point on the circle is at \((2, -1.5)\).

We can find the distance \(d\) between these two points using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting in the coordinates of the points:
- \( (x_1, y_1) = (-4, -1) \)
- \( (x_2, y_2) = (2, -1.5) \)

The distance calculation becomes:
\[
d = \sqrt{(2 - (-4))^2 + (-1.5 - (-1))^2}
\]
\[
= \sqrt{(2 + 4)^2 + (-1.5 + 1)^2}
\]
\[
= \sqrt{(6)^2 + (-0.5)^2}
\]
\[
= \sqrt{36 + 0.25}
\]
\[
= \sqrt{36.25}
\]
\[
\approx 6.031
\]

This distance represents the radius of the circle. The length of the diameter \(D\) is twice the radius:
\[
D = 2 \times d = 2 \times 6.031 \approx 12.062
\]

Rounding to the nearest tenth, the length of the diameter is:
\[
\boxed{12.1}
\]