On a number line, opposite refers to a number that is the same distance from zero but in the opposite direction, such as 5 and -5. This concept is crucial for understanding mathematical operations and physical movements in relation to a chosen reference point and direction, where positive and negative values apply.
Step-by-step explanation:
In mathematics, particularly on a number line, the term opposite refers to a numerical value that is the same distance from zero but in the reverse direction. On a number line, every position has an opposite. For example, the opposite of 5 is -5. These numbers are of equal distance from the origin (zero) but on opposite sides of the number line.
If you choose a positive direction in a calculation or representation, like towards Kevin's house, then the opposite direction, like towards the school, is represented as negative. This convention helps in understanding movements and displacements in physical problems. In addition, this also applies to other mathematical operations such as addition, subtraction, multiplication, and division, where combining numbers with opposite signs follows specific rules. For instance, subtracting a positive number is akin to adding its negative counterpart.
In graphical representations using Cartesian coordinates, this concept extends into two or three dimensions, assigning positive and negative values to directions based on the chosen axes. Therefore, understanding the concept of opposites on a number line is crucial for solving mathematical and physical problems accurately.