Question

question 2 of 25
graph the circle with center $(-1, 2)$ that passes through $(-6, 2)$. find the area 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 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 area in terms of $\pi$

Use the circle area formula $A = \pi r^2$.
$A = \pi (5)^2 = 25\pi$

Step3: Calculate numerical area

Substitute $\pi = 3.14$:
$A = 25 \times 3.14 = 78.5$

Answer:

Area in terms of $\pi$: $25\pi$
Area to the nearest tenth: $78.5$

(Note: For the graph, plot center $(-1,2)$, then draw a circle with radius 5 units. Using the scale of 2 per gridline, the radius will span 2.5 gridlines from the center in all directions.)