Question

In 2004, the world's largest carousel was located at the House on the Rock, in Spring Green, Wisconsin. Suppose that the center of the carousel is at the origin and that one of the animals on the circumference of the carousel has coordinates (24, 32). If one unit of the coordinate plane equals 1 foot, what is the diameter of the carousel

Answer 1

1. You have that the Standard form for the equation of a circle when its center is at the origin, is:

 x²+y²=r²

 2. You must calculate the radius. Then:

 r=√(x²+y²)

 x=24
 y=32

 3. When you substitute the values of "x" and "y" into the equation r=√(x²+y²), you obtain:

 r=√(x²+y²)
 r=√(24²+32²)
 r=√(576+1024)
 r=√1600
 r=40 feet

 4. Therefore, the diameter (D) of the circle, is:

 D=2r
 D=2(40 feet)
 D=80 feet