Question

a triangle with coordinates (2, 0), (6, 0), and (2, 2) is rotated 360° around the x - axis. what is the resulting three - dimensional figure? a cone with radius 2 and height 4 a cone with radius 4 and height 2 a triangular prism with side length 2 and height 4 a triangular prism with side length 4 and height 2

Explanation:

Step1: Analyze the triangle's properties

The points (2, 0) and (6, 0) lie on the x - axis. The distance between them is $d=6 - 2=4$, which will be the height of the 3 - D figure. The point (2, 2) has a y - coordinate of 2, and when rotated around the x - axis, this y - value represents the radius of the resulting 3 - D figure.

Step2: Recall rotation results

When a right - triangle is rotated 360° around one of its legs (lying on the x - axis in this case), the resulting three - dimensional figure is a cone.

Answer:

A. a cone with radius 2 and height 4