Final answer:
Placing two sides of a figure on the coordinate axes implies perpendicularity but does not specify the figure type; a free-body diagram uses a single point to represent an object; coordinate axes are mutually perpendicular, aiding in trigonometric calculations.
Step-by-step explanation:
When you place two sides of a figure on the coordinate axes, it generally implies that one side is aligned with the x-axis and the other with the y-axis. This doesn't confirm the type of figure specifically, but it does indicate that these sides are perpendicular to each other. Commonly, this practice is done to simplify calculations and to make use of the coordinate system's properties, such as using the axes as lines of symmetry or benchmarks for measuring distances and angles.
A free-body diagram represents the forces acting on an object by depicting the object as a single point, regardless of its actual shape or size. The forces are then shown as arrows emerging from this point, with each arrow labeled to indicate the type of force and its magnitude and direction.
In a coordinate system, the axes are by default mutually perpendicular to each other; this is a fundamental characteristic that defines the system. The positive direction of the y-axis is typically vertically upward, and the positive direction of the x-axis is horizontally to the right side. In the context of trigonometry, for a right triangle, the sine, cosine, and tangent functions are defined in terms of the triangle's sides relative to a specific angle as shown in the coordinate system.
Summarizing key concepts: understanding the relationship between a figure and the coordinate axes aids in mathematical analysis; a free-body diagram abstracts an object to a point to display its forces; the coordinate system is designed with perpendicular axes, and trigonometric functions relate to the sides of triangles within this system.