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High School Precalculus: Help and Review32 chapters | 297 lessons

Instructor:
*David Karsner*

Coordinate systems use 1-dimensional, 2-dimensional and 3-dimensional spaces and coordinates to define points. The ''xy'' coordinate grid is the most common of these systems, which you can learn how to use in this lesson.

Imagine that you are in New York City on a vacation and have picked up a sightseeing map. In looking for location of the Statue of Liberty, you see it has a designation of A3, or the meeting place of column A and row 3. Whether you realize it or not, you've just used a ** coordinate system**, which typically assigns numbers, or coordinates, to a point in space. Coordinate systems use one, two, or three coordinates representing 1-dimensional, 2-dimensional or 3-dimensional spaces.

A 1-dimensional coordinate system, also known as a **number line**, uses one coordinate to tell how far away from zero it is located. You can find an example of a 1-dimensional coordinate system below.

In a **2-dimensional coordinate system**, you use two values to give the location. The most commonly used coordinate system is called the ** xy coordinate grid**, which consists of two 1-dimensional number lines that intersect

All points within a 2-dimensional space are given by an **ordered pair** (*x,y*). The first number, or *x*, tells us how far to move from the origin along the *x*-axis, either left or right. Positive numbers move right, while negative numbers move left. The second number, or *y*, tells us how far to move along the *y*-axis, either up or down. Positive numbers move up, while negative numbers move down.

The *x*-axis and *y*-axis divide the coordinate plane into four sections known as **quadrants**, which are typically indicated by Roman numerals. In the upper-right, or **quadrant I**, both the *x* and *y* values are positive. **Quadrant II** is located in the upper-left corner; here, the *x* values are negative, while the *y* values are positive. In the bottom-left, or **quadrant III**, both the *x* and *y* values are negative. **Quadrant IV** is located in the bottom-right corner, where the *x* values are positive, and the *y* values are negative.

Take a look at the above image: do you see four points labeled A, B, C and D? Now, beginning at the origin, try to find point B(-3, 2). As the first number is -3, you'll move three place to the left. As the second number is 2, you'll move two places up to point B. You can try the exercise again using points, A, C and D.

There are other 2-dimensional coordinate systems that are not as common as the *xy* coordinate system. These include the **polar coordinate system**, where the *x*-axis and *y*-axis represent the distance from a point and the degree of rotation. In the **complex numbers system**, one axis represents the real part of a complex number, while the other axis represents the imaginary part of a complex number.

In a **3-dimensional coordinate system**, you use three coordinates to name a point in 3-dimensional space. In addition to the *x*-axis and *y*-axis, this system includes a *z*-axis. It looks just like a 2-dimensional coordinate system, with the exception of the third axis that lies perpendicular to the other two axes.

**Coordinate systems** use coordinates to assign a place in a 1-dimensional, 2-dimensional or 3-dimensional space. The ** xy grid** is the most common form of a 2-dimensional coordinate system, where the first coordinate directs motion along the

An *xy* graph is divided into four quadrants indicated by Roman numerals. In **quadrant I** and **quadrant II**, the numbers along the *x*-axis and *y*-axis are all positive or all negative respectively. In **quadrant II**, the *x* values are negative, while the *Y* values are positive. In **quadrant IV**, the *x* values are positive, and the *y* values are negative.

Less common 2-dimensional coordinate systems include **polar coordinate** and **complex number systems**. Other coordinate systems include a 1-dimensional **number line** and a **3-dimensional** system with a *z*-axis.

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High School Precalculus: Help and Review32 chapters | 297 lessons

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