Final answer:
To indicate positive and negative values, one can use number lines, graphical representations, rules of addition and subtraction, and figure/ground relationships in shapes. These representations assist in visualizing and understanding mathematical and geometrical concepts, stressing the importance of consistency in their application.
Step-by-step explanation:
To indicate positive and negative values, multiple representations can be used. These allow us to understand and visualize mathematical concepts, particularly in the context of coordinates, algebra, and geometry.
One representation involves using a number line or a coordinate system where a direction must be chosen as positive. For example, in a 1-dimensional frame of reference, we could denote the right direction as positive and the left direction as negative. This is analogous to choosing upwards as positive and downwards as negative in the context of vertical displacement.
In terms of shapes and figure/ground relationships, we can also talk about positive and negative values. The positive shapes could be considered the figures that we focus on, while the negative spaces are the ground or background that surrounds and defines these figures.
When it comes to operations with numbers, the rules of addition and subtraction apply differently to positive and negative numbers. For instance, the sum of two positive numbers will always be positive, e.g., 3+2 = 5. Conversely, when combining two negative numbers, the result is also negative, e.g., -4 + (-2) = -6. However, when adding numbers of opposite signs, the sign of the larger absolute value determines the sign of the result.
In graphical terms, drawing graphs for displacement or velocity over time is another way to represent positive and negative values. For example, if motion is considered negative, the velocity-time graph would slope downwards when velocity is plotted on the y-axis against time on the x-axis.
It is important to be consistent with the chosen representations to avoid confusion, especially when considering complex cases where multiple variables are involved or where the context of the problem dictates the conventions.