# 4.1.4: Coordinate Locations on a Map

- Page ID
- 4307

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Coordinate Locations on a Map

Ian finds an old map when he's going through his grandfather's attic. It seems to be a pirate map of the Spanish Main. On the back of it, he sees scrawled a hasty X and the numbers: 26.5 and 81. He suspects that this map leads to treasure. But where is it?

In this concept, you will learn how to use coordinates to locate a place on a map.

**Using Coordinates to Locate Places on Maps**

A **coordinate grid** is a grid in which points are graphed. It usually has two or more intersecting lines which divide a plane into **quadrants**, and in which ordered pairs, or coordinates, are defined.

Maps also use **coordinates**. Around the edges of maps are numbers and sometimes letters. These define the location of cities, states, and other physical entities and landmarks. Most maps use degrees. These define the **latitude** and **longitude**.

**Longitude** is the measure, in degrees, of lines vertically on a map. Depending on how the map is made, these lines are sometimes curved.

**Latitude** is the measure, in degrees, of lines horizontally on a map.

These degrees are written as ordered pairs with the latitude listed first and the longitude listed second. Here is an example of a world map with the latitude and longitude lines overlaid on it. For lines to the left of 0° or below the equator, there is in implied negative sign. Sometimes coordinates are also written with directions. 30°S is the latitude line beneath the Tropic of Cancer on the map below.

You can identify different locations on a map if you have the coordinates of the location. For example, which country is located at 30°, 140°?

First, identify the latitude line.

In this case, it is below the Tropic of Capricorn line and it goes through Australia and South America.

Next, identify the longitude line.

In this case, it is off to the right and it seems to go mainly through eastern Europe and Australia.

Then, decide where they converge.

In this example, they both pass through Australia, so that is the country that exists at those coordinates.

**Examples**

Example 4.1.4.1

Earlier, you were given a problem about Ian and his pirate treasure.

He has found a map with what he suspects are coordinates pointing to pirate treasure, but he doesn't know where to dig. The coordinates say 26.5 and 81.

**Solution**

First, he decides which coordinate is which.

26.5 must be the latitude because the numbers don't go that low on the bottom. That means that 81 is the longitude.

Next, he locates the latitude and then the longitude of the point.

That latitude seems to go through the Atlantic Ocean and some islands.

That longitude seems to go up through Cuba and then Florida.

Then, he finds where they converge.

They seem to meet up in the Florida Keys.

He concludes that the booty is in the Keys. He starts dreaming up get-rich-quick schemes that will get him to Florida so he can start digging.

Example 4.1.4.2

In the map above, identify the state found at (40°N, 80°W).**Solution**

First, find the latitude. This is the horizontal line.

In this case, it is 40°N. This line goes through the middle of the map. It crosses Montana, Illinois, Indiana, Ohio, and Pennsylvania.

Next, find the longitude.

In this case it is 80°W. Starting in South Carolina, it goes up through North Carolina, Virginia, West Virginia, and Pennsylvania.

Then, find the state where they converge.

Pennsylvania is the only state that both lines go through, so it is the answer.

**In the following examples, use the map of the world below to identify the countries given by the corresponding latitude and longitudes.**

Example 4.1.4.4

(0°, 60°W)

**Solution**

First, find the latitude. This is the horizontal line.

In this case, it is 0°, which is also known as the equator.

Next, find the longitude.

In this case it is 60°W. It is in what we call the "Western Hemisphere", and it mostly passes through South America.

Then, find where they converge.

In this case, they converge in Brazil.

Example 4.1.4.4

(35°N, 90°W)

**Solution**

First, find the latitude. This is the horizontal line.

In this case, it is 35°N. It is above 30°N in the Northern Hemisphere. It goes through North America, Africa, and Asia.

Next, find the longitude.

In this case it is 90°W. It goes mostly through Central and North America.

Then, find where they converge.

In this case, they converge in the United States.

Example 4.1.4.5

(35°N, 90°E)

**Solution**

First, find the latitude. This is the horizontal line.

In this case, it is 35°N. It is above 30°N in the Northern Hemisphere. It goes through North America, Africa, and Asia.

Next, find the longitude.

In this case it is 90°E. It goes up through Asia.

Then, find where they converge.

In this case, they converge in China.

### Review

Use a map of the United States to identify each city on the map according to latitude and longitude.

- What is at 61
^{∘},149^{∘}? - What is at 30
^{∘},97^{∘}? - What is at 39
^{∘},71^{∘}? - What is at 41
^{∘},87^{∘}? - What is at 41
^{∘},81^{∘}? - What is at 21
^{∘},157^{∘}? - What is at 44
^{∘},123^{∘}? - What is at 30
^{∘},81^{∘}? - What is at 36
^{∘},115^{∘}? - What is at 34
^{∘},118^{∘}? - What is at 35
^{∘},78^{∘}? - What is at 37
^{∘},77^{∘}? - What is at 38
^{∘},90^{∘}? - What is at 27
^{∘},82^{∘}? - What is at 38
^{∘},77^{∘}?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 11.16.

### Vocabulary

Term | Definition |
---|---|

x−axis |
The x−axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable. |

y axis |
The y-axis is the vertical number line of the Cartesian plane. |

Latitude |
Latitude is a coordinate that specifies the north-south location of a point on the Earth's surface. |

Longitude |
Longitude is a coordinate that specifies the east-west location of a point on the Earth's surface. |

Ordered Pair |
An ordered pair, (x,y), describes the location of a point on a coordinate grid. |

Origin |
The origin is the point of intersection of the x and y axes on the Cartesian plane. The coordinates of the origin are (0, 0). |

Quadrants |
A quadrant is one-fourth of the coordinate plane. The four quadrants are numbered using Roman Numerals I, II, III, and IV, starting in the top-right, and increasing counter-clockwise. |

### Additional Resources

Practice: **Coordinate Locations on a Map**