Question

graph the circle with center (4, 1) that passes through (4, -4). 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 \((4, 1)\) and the point \((4, -4)\) on the circle. Since the \( x \)-coordinates are the same, we use the distance formula for vertical distance: \( |y_2 - y_1| \).
\( r = | - 4 - 1| = | - 5| = 5 \)

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

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

Step3: Calculate circumference to the nearest tenth

Using \( \pi = 3.14 \), substitute into \( C = 10\pi \):
\( C = 10 \times 3.14 = 31.4 \)

Answer:

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