Question

a figure is located at (0, 0), (-3, -4), and (-3, 0) on a coordinate plane. what kind of 3 - d shape would be created if the figure was rotated around the x - axis? provide an explanation and proof of your answer to receive full credit. include the dimensions of the 3 - d shape in your explanation.

Explanation:

Step1: Identify the 2 - D figure

The points (0, 0), (-3, -4), and (-3, 0) form a right - triangle in the coordinate plane. The vertical side has length 4 (distance from y = 0 to y=-4) and the horizontal side has length 3 (distance from x = 0 to x=-3).

Step2: Recall rotation rules

When a right - triangle is rotated about one of its legs (in this case, the x - axis which is one of the legs of the right - triangle), it forms a cone.

Step3: Determine the dimensions of the cone

The radius of the base of the cone is the length of the non - axis leg of the right - triangle. Here, the radius $r = 4$ (the vertical side length). The height of the cone $h=3$ (the horizontal side length).

Answer:

The 3 - D shape created is a cone with radius $r = 4$ and height $h = 3$.