Coordinate Graphs

Each point on a number line is assigned a number. In the same way, each point in a plane is assigned a pair of numbers. These numbers represent the placement of the point relative to two intersecting lines. In coordinate graphs (Figure 1), two perpendicular number lines are used and are called coordinate axes. One axis is horizontal and is called the x‐axis. The other is vertical and is called the y‐axis. The point of intersection of the two number lines is called the origin and is represented by the coordinates (0,0).
Figure 1. Coordinate graph.

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Each point on a plane is located by a unique ordered pair of numbers called coordinates. Some coordinates are noted in Figure 2.

Figure 2. Coordinate graph showing some coordinates.

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Notice that on the x‐axis, numbers to the right of 0 are positive and to the left of 0 are negative. On the y‐axis, numbers above 0 are positive and below 0 are negative. Also note that the first number in the ordered pair is called the x‐coordinate, or abscissa, while the second number is the y‐coordinate, or ordinate. The x‐coordinate shows the right or left direction, and the y‐coordinate shows the up or down direction.

The coordinate graph is divided into four quarters called quadrants. These quadrants are labeled in Figure 3.

Figure 3. Coordinate graph with labeled quadrants.

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Notice that

  • In quadrant I, x is always positive and y is always positive.
  • In quadrant II, x is always negative and y is always positive.
  • In quadrant III, x and y are both always negative.
  • In quadrant IV, x is always positive and y is always negative.

Example 1

Identify the points ( A, B, C, D, E, and F) on the coordinate graph shown in Figure 4.

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