Question

a sporting goods company produces an archery target. the scale drawing of the plan shows the center at (-1.5, 3.5) and one point on the circle at (8, 9). what is the approximate area of the target in units on the scale drawing? use 3.14 for $pi$, and round the answer to the nearest whole number

Explanation:

Step1: Find the radius

The distance between the center $(-1.5,3.5)$ and the point on the circle $(8,9)$ is the radius $r$. Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
$r=\sqrt{(8-(-1.5))^2+(9 - 3.5)^2}=\sqrt{(9.5)^2+(5.5)^2}=\sqrt{90.25 + 30.25}=\sqrt{120.5}\approx10.98$.

Step2: Calculate the area

The area of a circle is $A=\pi r^2$. Substitute $\pi = 3.14$ and $r\approx10.98$.
$A=3.14\times(10.98)^2=3.14\times120.5604\approx378$.

Answer:

$378$ units$^2$