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## Introduction

In the game of Battleship, your goal is to figure out where your opponent’s fleet of ships is located, then sink each ship by firing at its coordinates on a map.  If you have ever played this game, there are letter coordinates and number coordinates.  The coordinate B-6 means to go over to “B” and up to “6”.  The letter tells you how far to move to the right and the number tells you how far to move up.  Using numbers and letters, you have the opportunity to guess where their ships might be anywhere on their entire map.

Plotting points in mathematics follows the same logic.  You begin from a central point on the coordinate axis called the origin.  The coordinate plane contains the same two directional movements as the game of Battleship.  First move left or right, then move up or down.

## Lesson

When you first learned about numbers, a number line provided an excellent visual representation of the numbers.  Later, you learned to separate the numbers into positive numbers and negative numbers.  The number line below demonstrates the difference between positive and negative numbers.

One important fact is that all numbers to the right of zero are positives, while all numbers to the left of zero are negatives.  In the diagram, larger numbers are further away from the middle of the graph than smaller numbers.  This graph is one-dimensional and is limited to going exactly left or right.

A coordinate plane represents two separate values, an x-value and a y-value.  When looking at a coordinate plane, the x-axis corresponds to the number line.  A second coordinate determines how far up or down to go in order to get the location of the point.

Consider the point (3, 6).  This point can be found by moving over  3 and up  6.

The first number is done exactly the same as if it were on a number line.  The number “3” is three to the right of the starting point.

Every coordinate can be represented by the notation (x, y) where x represents the horizontal location and y represents the vertical location on the graph.  Here are the graphs of some various points on the coordinate plane.

So each coordinate can be found using two separate values, each one representing a direction and a distance.  The first value represents the distance left or right from the starting point.  The second value represents the distance up or down from the starting point.  Putting these two coordinates together allows for any point on the coordinate plane to be represented.  The two numbers are generally written inside parenthesis and separated by a comma.

An easy way to begin plotting coordinates shown to the left.  When considering the first coordinate, move right for a positive and left for a negative.  The second coordinate tells you to move up for a positive and down for a negative.

*Move up (positive) or down (negative) to get to the second coordinate.

The coordinate plane can be divided into four separate quadrants.  There are four different ways that coordinates can be named using positives and negatives, and each of these quadrants represents one of these results.  The game of battleship uses only positive letters and positive numbers, so all points on the battleship board would be contained in the top right quadrant.  This quadrant is represented with the Roman numeral I.

Finding and graphing coordinates is a skill that you can pick up quickly.  Once you get used to moving over first and up second, finding the correct location of coordinates simply requires that you be precise when pinpointing their exact location.  Take your time and count carefully, especially for coordinates containing larger numbers.

## Try It

Find the coordinate of each point.

1) A                            2)  B                            3)  C

4)  D                           5)  E                            6)  F

Solutions:

1) A is (-6, 6)                         2)  B is (5, 8)

3)  C is (7, -2)                        4)  D is (-7, -8)

5)  E is (-8, 0)                        6)  F is (0, 7)