Question

question 1 of 9
graph the circle with center (-3, -3) that passes through (2, -3). find the circumference in terms of π and to the nearest tenth. use 3.14 for π.
attention: the graphs in the answer choices use a scale of 2 on both the x- and y-axes (i.e., the distance between gridlines is 2 units).

Explanation:

Step1: Find the radius

The radius \( r \) is the distance between the center \((-3, -3)\) and the point \((2, -3)\) on the circle. Using the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \), since the \( y \)-coordinates are the same, the distance is just the difference in \( x \)-coordinates. So \( r = |2 - (-3)| = |2 + 3| = 5 \).

Step2: Calculate the circumference in terms of \( \pi \)

The formula for the circumference of a circle is \( C = 2\pi r \). Substituting \( r = 5 \), we get \( C = 2\pi \times 5 = 10\pi \).

Step3: Calculate the circumference to the nearest tenth

Using \( \pi \approx 3.14 \), we have \( C \approx 10 \times 3.14 = 31.4 \).

Answer:

In terms of \( \pi \), the circumference is \( 10\pi \). To the nearest tenth, the circumference is \( 31.4 \).