This lesson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. In this lesson, we will learn:

- xy-coordinate system
- four quadrants
- ordered pair
- plot points on the coordinate plane
- reflection of points about the
*x*-axis,*y*-axis and origin

Two real number lines that are perpendicular to each other and that intersect at their respective zero points define a rectangular coordinate system, often called the *xy*-coordinate system or *xy*-plane. The horizontal number line is called the x-axis and the vertical number line is called the y-axis. The point where the two axes intersect is called the origin, denoted by O. The positive half of the *x*-axis is to the right of the origin, and the positive half of the *y*-axis is above the origin. The two axes divide the plane into four regions called quadrants I, II, III, and IV, as shown in the figure below.

Each point P in the xy-plane can be identified with an ordered pair (*x*, *y*) of real numbers and is denoted by P(*x*, *y*). The first number is called the *x*-coordinate, and the second number is called the *y*-coordinate. A point with coordinates (*x*, y) is located x units to the right of the *y*-axis if *x* is positive or to the left of the *y*-axis if *x* is negative. Also, the point is located y units above the *x*-axis if *y* is positive or below the *x*-axis if *y* is negative. If the point lies on the *y*-axis, and if the point lies on the *x*-axis. The origin has coordinates (0, 0). Unless otherwise noted, the units used on the *x*-axis and the *y*-axis are the same.

In the following coordinate plane: .

Point *M* has coordinates (2, 1.5). To get to point *M*, we move 2 units to the right (positive) and 1.5 units up (positive).

Point *L* is represented by the coordinates (–3, 1.5). To get to point *L,* we move 3 units to the left (negative) and 1.5 units up (positive)

Point *N* has coordinates (–2, –3). To get to point *N*, we move 2 units to the left (negative) and 3 units down (negative).

**Coordinate plane or Cartesian plane, quadrants**

How to plot points on the Cartesian plane?

**How to find the ordered pair or coordinates of a given point?**

How to plot the point given the ordered pair or coordinates?

In the diagram below, the three points *A*’ (3, −2), *A*’’ (−3, 2), *A*’’’ (−3, −2) are geometrically related to *A* (3, 2) as follows.

• *A*’ is the reflection of *A* about the x-axis, or *A*’ and *A* are symmetric about the x-axis.

• *A*’’ is the reflection of *A* about the y-axis, or *A*’’ and *A* are symmetric about the y-axis.

• *A*’’’ is the reflection of *A* about the origin, or *A*’’’ and *A* are symmetric about the origin.

**Reflect a Point about the x-axis, y-axis, and the Origin**

This video provides an example of how to determine the coordinates of a point reflected about the x-axis, y-axis, and the origin.

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