Question

2b. if the polygon shown below is rotated about the y - axis, what will be the height of the 3 - dimensional figure that is created?

Explanation:

Step1: Identify the 3 - dimensional figure

When a right - triangle (in this case, triangle \(ABC\)) is rotated about one of its legs (the \(y\) - axis, which is side \(AB\)), the resulting 3 - dimensional figure is a cone.

Step2: Determine the height of the cone

The height of a cone formed by rotating a right - triangle about one of its legs is the length of that leg.
The length of segment \(AB\) can be calculated using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(A(0,0)\) and \(B(0,5)\), \(d=\sqrt{(0 - 0)^2+(5 - 0)^2}=5\)

Answer:

\(5\)