Question

A 2-dimensional figure is graphed on the coordinate plane with vertices at (0,5), (3, 5), and (0,20)

Part A: What is the figure?
Part B: When the figure is rotated along the y-axis to create a 3-dimensional figure, what does it form?

Answer 1

A. Right-Triangle
B. Right Circular Cone

Explanation:

A. Any set of three points(other than if all points are colinear) will form a triangle of some sorts. In this case, we see that the base is formed from the points (0,5) and (3,5), whereas the peak is (0,20). Since the left base and the peak have the same x-coordinate, a right angle must be formed.

B. Visually, if we rotate a triangle infinitely around the y-axis, the shape formed is that of a cone(imagine the triangle spinning around the y-axis, and the funnel-like shape comes to life).