Question

question 9 of 25
graph the circle with center (-1, 2) that passes through (-6, 2). find the circumference in terms of $pi$ and to the nearest tenth. use 3.14 for $pi$.
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: Calculate the circle's radius

The radius $r$ is the distance between center $(-1,2)$ and point $(-6,2)$. Using the distance formula for horizontal points:
$r = |-1 - (-6)| = |5| = 5$

Step2: Find circumference in terms of $\pi$

Use circumference formula $C = 2\pi r$:
$C = 2\pi \times 5 = 10\pi$

Step3: Calculate decimal circumference

Substitute $\pi = 3.14$:
$C = 10 \times 3.14 = 31.4$

Answer:

Circumference in terms of $\pi$: $10\pi$
Circumference to the nearest tenth: $31.4$

(For graphing: Plot center $(-1,2)$, then mark points 5 units away in all directions. With an axis scale of 2 units per gridline, the circle will extend 2.5 gridlines left/right/up/down from the center.)