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The coordinate plane is a two-dimensional surface where each point is defined by a pair of numbers known as coordinates. These numbers correspond to the horizontal and vertical positions, respectively, on the plane. A coordinate plane is divided into four quadrants by the x-axis (horizontal line) and y-axis (vertical line), which intersect at the origin, marked as (0,0).

Points on the coordinate plane are written as \( (x, y) \) where \( x \) represents their horizontal distance from the origin, and \( y \) represents their vertical distance. Understanding the coordinate plane is crucial as it is the foundation for graphing equations, determining the location of points, and calculating distances between points.

Subtracting coordinates enables us to find the distance and direction from one point to another on the coordinate plane. When subtracting coordinates, it's important to carefully consider the signs (+ or -) of the values you're working with.

To subtract coordinates and find the directed distance between two points, simply subtract the corresponding x or y values, depending on whether you're measuring horizontal or vertical distance. For example, if you have two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) and you want to find the vertical distance from \( A \) to \( B \) you would calculate \( B_y - A_y \) where \( B_y \) and \( A_y \) are the y-coordinates of points \( B \) and \( A \) respectively.

Vertical movement in the context of a coordinate plane refers to motion along the y-axis. This vertical motion is either upwards or downwards relative to the origin's position. When the y-coordinate increases, the movement is upwards, and when it decreases, it's downwards.

Assessing vertical movement is essential, especially when determining the directed distance between points that have the same x-coordinates. This scenario indicates that there has been no horizontal movement, and the directed distance is purely vertical. Always remember that the result of subtracting y-coordinates will indicate the direction: a positive result points upwards, and a negative result points downwards on the axis.