# Coordinate Systems

- Author:
- Judith Hilinski

- Topic:
- Geometry

**According to the Ruler Postulate, the points on a line can be numbered so that to every point there is matched number called its coordinate.**

**A line numbered in this way is a one dimensional coordinate system (number line).**

## One Dimensional Coordinate System

**If two lines are numbered according to the Ruler Postulate are perpendicular to one another (as shown in the figure below) the number lines become the axes of a two dimensional coordinate system.**

**The axes are labeled x and y, and the point in which they intersect, zero on each axis, is labeled with a capital O and is the origin of the coordinate system.**

**The axes separate the**

**plane**

** that contains them into four parts (quadrants). The quadrants are identified by Roman numerals.**

Roman Numeral | Counting Number |

I | 1 |

II | 2 |

III | 3 |

IV | 4 |

**To find the coordinates of any given point on a coordinate plane, locate the point and draw a perpendicular line from the point to the x axis. That is the point's x coordinate. Return to the same point and draw a perpendicular line from the point to the y axis. That is the point's y coordinate.**

## How to find the coordinates of a point

**Definitions**The x-coordinate of a point is the number located on the x-axis (back and forth line)

**The y-coordinate of a point is the number located on the y-axis (up and down line) The coordinates of a point are written in parentheses and separated by a comma The x coordinate is ALWAYS listed first (x,y)**

## The following exercises refer to the figure below.

## Question 1

**What are the lines labeled x and y called?**

Check all that apply

- A
- B
- C
- D

## Question 2

**What is the point labeled O called?**

Check all that apply

- A
- B
- C
- D

## Question 3

**Which quadrant is point P in?**

Check all that apply

- A
- B
- C
- D

## Question 4

**What is the x-coordinate of point P?**

Check all that apply

- A
- B
- C
- D

## Question 5

**What is the y-coordinate of point P?**

Check all that apply

- A
- B
- C
- D