**The Rectangular Coordinate Plane**

This section explains the concepts of combining algebra and geometry using the **rectangular coordinate plane** .

The rectangular coordinate plane uses two perpendicular number lines called **axes** . The horizontal axis is called the **x axis** . The vertical axis is called the **y axis** . The intersection of the axes is called the **origin** . The axes divide the plane into four **quadrants** , called I, II, III, and IV (see Fig. 11-1).

**Plotting Points**

Each point on the plane can be located by its **coordinates** . The coordinates give the horizontal and vertical distances from the y axis and x axis, respectively. The distances are called the **x coordinate (abscissa)** and the **y coordinate (ordinate)** , and they are written as an **ordered pair** (x, y). For example, a point with coordinates (2, 3) is located two units to the right of the y axis and 3 units above the x axis (see Fig. 11-2 ).

The point whose coordinates are (2, 3) is located in the first quadrant or QI, since both coordinates are positive. The point whose coordinates are (–4, 1) is located in the second quadrant or QII, since the x coordinate is negative and the y coordinate is positive. The point whose coordinates are (–3, –5) is in the third quadrant or QIII, since both coordinates are negative. The point (3, –1) is located in the fourth quadrant or QIV, since the x coordinate is positive and the y coordinate is negative (see Fig. 11-3).

The coordinates of the origin are (0, 0).

Any point whose y coordinate is zero is located on the x axis. For example, point P, whose coordinates are (–3, 0), is located on the x axis 3 units to the left of the y axis. Any point whose x coordinate is zero is located on the y axis. For example, the point Q, whose coordinates are (0, 4), is located on the y axis four units above the x axis (see Fig. 11-4).

**Example**

Give the coordinates of each point shown in Fig. 11-5 .

**Solution**

A (–2, 4); B (3, 1); C (–1, –5); D (6, –2); E (2, 0); F (0, –4).

**The Coordinate Plane and Plotting Points Practice Problems**

**Practice**

Give the coordinates of each point shown in Fig. 11-6 .

**Answers**

1. A (–4, –2)

2. B (2, –5)

3. C (–3, 4)

4. D (1, 5)

5. E (5, 0)

6. F (0, –1)

Practice problems for these concepts can be found at: Graphing Practice Test.

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