Definition: A-axis, or vertical axis in a Cartesian coordinate system, refers to the x-coordinate in a 2D plane. It is the horizontal line that marks the position along which a point moves when it is plotted on a graph of the Cartesian coordinate system. In the Cartesian coordinate system (also known as Euclidean geometry), the x-axis represents the horizontal direction while the y-axis represents the vertical direction. The x-axis is always perpendicular to the y-axis, and both axes intersect at the origin (0, 0). The coordinates of a point can be represented on the x-axis as x=0, and on the y-axis as y=0. This is known as the rectangular coordinate system. A-Axis in Euclidean geometry represents all points that are equidistant from a given line. In mathematics, a point (p) is said to have a positive x-coordinate if p lies to the left of the y-axis and a negative x-coordinate if it lies to the right. A negative value for x indicates an object to the right of the origin. Similarly, a positive value for x indicates an object to the left of the origin. A-Axis in Euclidean geometry refers to all points that are equidistant from a given line (the y-axis). This concept is known as the distance formula, which relates two points on a coordinate plane to the shortest distance between them. The equation for this is: d = |x1 - x2| + |y1 - y2| Where d represents the distance between the two points, and x1 and y1 represent the coordinates of point 1, and x2 and y2 represent those of point 2. The negative value of x indicates an object to the right of the origin, while the positive value indicates an object to the left. In this context, we refer to the positive x axis as "positive" because it represents a direction that is moving inwards towards the origin (0,0). In summary, the A-axis is the vertical line perpendicular to the y-axis and passes through the origin. It is represented by the point (0, 0), while the x-axis is represented by the points (-x, -y) or by positive values (positive x axis) if it is pointing towards the origin (0,0).