Question

a new merry - go - round is being installed on the fairgrounds. a scale of the plans is drawn on a coordinate plane with the center at (-3, 5) and a point on the circle at (-8, -2). what is the approximate length in units on the scale drawing of the merry - go - rounds edge? use 3.14 for π, and round your answer to the nearest tenth.
54.0 units
40.9 units
27.0 units
81.9 units

Explanation:

Step1: Find the radius

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(-8,-2)$.
$r=\sqrt{(-8 + 3)^2+(-2 - 5)^2}=\sqrt{(-5)^2+(-7)^2}=\sqrt{25 + 49}=\sqrt{74}\approx8.6$.

Step2: Find the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Substitute $r\approx8.6$ and $\pi = 3.14$.
$C=2\times3.14\times8.6 = 54.008\approx54.0$.

Answer:

54.0 units