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:
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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