Question

graph the circle with center (-3, -3) that passes through (2, -3). find the area 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 absolute difference of the \( x \)-coordinates. So \( r = |2 - (-3)| = |2 + 3| = 5 \).

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

The formula for the area of a circle is \( A = \pi r^2 \). Substituting \( r = 5 \), we get \( A = \pi (5)^2 = 25\pi \).

Step3: Calculate the area using \( \pi = 3.14 \)

Substitute \( \pi = 3.14 \) into \( 25\pi \). So \( A = 25\times3.14 = 78.5 \).

Answer:

The area in terms of \( \pi \) is \( 25\pi \) and to the nearest tenth (using \( \pi = 3.14 \)) is \( 78.5 \).