Question

graph the circle with center (2, -3) that passes through (2, 0). 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 \((2, -3)\) and the point \((2, 0)\) on the circle. Using the distance formula for vertical points (\(x\)-coordinates are the same), \( r = |y_2 - y_1| = |0 - (-3)| = 3 \).

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

The formula for the circumference of a circle is \( C = 2\pi r \). Substituting \( r = 3 \), we get \( C = 2\pi \times 3 = 6\pi \).

Step3: Calculate circumference to the nearest tenth

Using \( \pi \approx 3.14 \), \( C = 2 \times 3.14 \times 3 = 18.84 \). Rounding to the nearest tenth, \( 18.84 \approx 18.8 \).

Answer:

In terms of \( \pi \): \( 6\pi \)
To the nearest tenth: \( 18.8 \)