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# Coordinate Geometry Study Guide

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Updated on Oct 5, 2011

## Introduction to Coordinate Geometry

### Lesson Summary

In this lesson, you will learn to identify the x-axis, y-axis, the origin, and the four quadrants on a coordinate plane. You will also learn how to plot or graph points on a coordinate plane and name the coordinates of a point. The distance between two points will also be found using a formula.

I you have ever been the navigator on a road trip, then you have probably read a road map or grid map. A grid map uses a horizontal and vertical axis in a similar manner as a coordinate plane.

## The Coordinate Plane

On a coordinate plane, the horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the two axes cross is called the origin.

The two axes divide the coordinate plane into four regions, which are called quadrants. The quadrants are numbered counterclockwise beginning with the upper-right region. The coordinates (x,y) of a point are an ordered pair of numbers. The first number is the x-coordinate. The second number is the y-coordinate. The coordinates of the origin are (0,0).

#### Example:

Graph point A(–4,1) and point B(5,–3). In which quadrant would you find each point?

#### Solution:

To graph point A(–4,1), from the origin, go left 4 units and up 1. Label the point A. Point A is in quadrant II. To graph point B(5,–3), start from the origin, then go right 5 units and down 3. Label the point B. Point B is in quadrant IV.

### Points Graphed on the Axes

Some points may be graphed on the axes also.

#### Example:

Graph point C(2,0) and point D(0,–6). On which axis will each point lie?

#### Solution:

To graph point C, from the origin, go right 2 units, but do not move up or down. Label the point C. Point C is on the x-axis. To graph point D, from the origin, do not move right or left; move 6 units down. Label the point D. Point D is on the y-axis.

## Finding the Coordinates of a Point

Each point on the coordinate plane has its own unique ordered pair. You can think of an ordered pair as an address. Now that you have located a point, you can also find the coordinates of a point on a graph.

#### Example:

Find the coordinates of each point.

#### Solution:

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

## Finding the Distance between Two Points

You can easily count to find the distance between two points on a horizontal or vertical line. For example, in the following figure, However, you cannot find simply by counting. Since ΔXYZ is a right triangle, you can use the Pythagorean theorem.

Of course, you won't be able to use the Pythagorean theorem all the time. However, you can use the following formula to find the distance between any two points.

#### Example:

Find the distance between R(–3,4) and S(–3,–7).

#### Solution:

It helps to label the coordinates of the points before you insert them into the formula.

Practice problems for these concepts can be found at: Coordinate Geometry Practice Questions.

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