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.

Answer 1

Answer:

cone

Step-by-step explanation:

Define the given points:

• A = (0, 0)
• B = (-3, -4)
• C = (-3, 0)

As two points have the same x-coordinate and two different points have the same y-coordinate, the 2D shape the points make is a right triangle (see first attached diagram).

As points B and C lie on the same vertical line (x = -3), and point C lies on the x-axis, rotating line segment BC about the x-axis will produce a circle with center C and radius BC (4 units).

As point A lies on the x-axis, it will not move when rotated about the x-axis.

Therefore, the 3D shape the triangle will create is a cone with:

• vertex at (0, 0)
• center of circular base at (-3, 0)
• radius of circular base of 4 units
• height of 3 units

(see second attached diagram)