Accessibility Note: This document is provided as accessible alternative media for an animation introducing two-dimensional and three-dimensional coordinate systems in virtual spaces. It presents equivalent descriptive and explanatory content in text form.
This document combines descriptive information about what occurs in the animation with explanations of the underlying concepts. It is intended to provide a complete, standalone description of how positions in two- and three-dimensional spaces are represented using coordinates.
---Description: A black computer screen appears. A red square is near the bottom-left. A point marks the origin. Arrows extend to the right and upward, labeled x and y. Coordinate values appear in the top-right.
Explanation: On a computer screen, every object has a position. We describe that position using a coordinate system. The system begins at a point called the origin. From it, we define horizontal x and vertical y directions. Every position is described by two numbers.
Description: The square moves to the right, then back toward the origin. It continues left past the origin and eventually moves off the visible screen. It then returns to the origin.
Explanation: As the square moves to the right, the x value increases. As it moves back toward the origin, the x value decreases. When it passes to the left of the origin, the x value becomes negative. The square can move off the screen, but its position is still defined by its coordinates.
Description: The square moves upward and then downward. It passes below the origin and moves off-screen before returning.
Explanation: Moving upward increases the y value. Moving downward decreases it. When the square moves below the origin, the y value becomes negative. Even when the square is not visible, its position is still defined.
Description: The square remains within a coordinate system that extends beyond the visible screen.
Explanation: The screen shows only part of a larger coordinate system. Every position—visible or not—can still be described using x and y values.
Description: The square extends into a cube. The view shifts to show depth. A third axis appears, pointing toward the viewer. A transparent plane indicates vertical reference. Coordinate values update to include x, y, and z.
Explanation: The system is extended into three dimensions. A third direction, called the z-axis, is added. This axis measures depth—how far an object is in front of or behind the origin. Positions are now described by three numbers: x, y, and z.
Description: A right hand enters the scene. The thumb points right, the index finger points upward, and the middle finger points outward toward the viewer. The hand then exits.
Explanation: These directions form a right-handed coordinate system. The thumb represents positive x, the index finger represents positive y, and the middle finger represents positive z.
Description: The cube moves right and left, then up and down, passing above and below a transparent plane.
Explanation: Movement along the x-axis increases or decreases the x value, just as in two dimensions. Movement along the y-axis increases or decreases the y value, including positions below the origin.
Description: The cube moves toward the viewer and appears larger. It continues forward until it passes beyond the viewer’s position and leaves view. It then returns, passes through the origin, and moves away, appearing smaller.
Explanation: The z-axis describes depth. Moving toward the viewer increases the z value. When the cube passes beyond the viewer, it is no longer visible, but its position continues to change. Moving away from the viewer produces negative z values.
Description: The cube moves in and out of view in depth, similar to how the square moved off-screen earlier.
Explanation: Just as objects can move off-screen in two dimensions, they can also move out of view in depth. In both cases, coordinates still define their position.
Description: The cube moves diagonally through space, occupying positions where all coordinates are positive and then all are negative.
Explanation: In three dimensions, all three coordinates can change at once. Every position is defined by a combination of x, y, and z values.
Description: The viewpoint moves around the cube while the cube and coordinate system remain fixed. The same object appears differently from different angles.
Explanation: The viewer also has a position in this space. As the viewpoint changes, the object stays in the same place. The coordinate system does not move—only the observer’s perspective changes.
Description: The viewpoint is positioned in front of the origin.
Explanation: In this view, the observer is located in front of the origin, where x, y, and z are positive. This is why moving toward the viewer increases the z coordinate.
Description: The cube returns to the origin. The coordinate axes remain visible. The coordinate values return to zero.
Explanation: A coordinate system allows any position in space to be described using numbers. Whether visible or not, every location can be represented using x, y, and z coordinates.