Final answer:
Completing the chart involves plotting points on a graph using a Cartesian coordinate system, applying transformations to the coordinates, and potentially extending the process to 3D space by including a z-coordinate.
Step-by-step explanation:
Completing the chart with the coordinates of the points provided given the transformation described involves plotting the data onto a Cartesian coordinate system. First, you would identify the x-axis and y-axis on the graph. Next, for each data point, you would locate the x-coordinate on the x-axis and then move vertically to find the y-coordinate, placing a dot where these two meet. When calculating change, often labeled as (Δ), you subtract the initial value from the final value. This could involve finding differences in distances, temperatures (for physics problems), or other quantities depending on the context. To plot a point given the transformation, you would apply the rules of the transformation to the x and y coordinates. For example, a transformation might consist of a translation, rotation, reflection, or dilation. The transformed coordinates are then used to plot the point on a new graph. For 3-dimensional space, you would extend this process by adding a third coordinate, z, which indicates the height above or depth below the plane formed by the x and y axes. By combining these three coordinates, you can locate points in 3-dimensional space. The labeling conventions are the same as in 2 dimensions, with positive numbers representing distances to the right, up, or outwards (away from the observer) from the origin, and negative numbers representing distances in the opposite directions.