Question

question 10 of 10
graph the circle with center (2, -3) that passes through (2, 0). 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 center of the circle is \((2, -3)\) and it passes through \((2, 0)\). The radius \(r\) is the distance between these two points. Using the distance formula for vertical points (\(x\)-coordinates are the same), \(r=\vert0 - (-3)\vert=\vert3\vert = 3\).

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

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = 3\), we get \(A=\pi\times3^{2}=9\pi\).

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

Substitute \(\pi = 3.14\) into \(A = 9\pi\), so \(A=9\times3.14 = 28.26\). Rounding to the nearest tenth, we look at the hundredth place (6), which is greater than 5, so we round up the tenth place. \(28.26\approx28.3\).

Answer:

• Area in terms of \(\pi\): \(9\pi\)
• Area to the nearest tenth: \(28.3\)