This lecture outlines how to make measurements on a map, particularly focusing on coordinate systems used to determine the location of features. It details the differences between geographic and projected coordinate systems, and outlines the steps to accurately determine and plot locations using mathematical coordinates. The lecture emphasizes the practical applications of these measurements for locating features, project siting, and navigation.

1. Lecture 5: Making
measurements on a map
By G.A.B. Yiran

2. objectives
• By the end of this lecture, you should be able to:
1. Be able to make measurements of coordinates
2. To understand why we make these measurements or to
understand the uses of the measurements

3. Coordinate Systems
• They are map Reference Systems or MODELS used to
determine the location of features in the real world or
on a map
• A geographic coordinate system attempts to model the
shape of the earth as accurately as possible based on
varying models of the shape of the earth
• No system is completely accurate (therefore the need to
be familiar with their properties)
3

4. The Shape of the Earth
4

5. Figure ..Graticules showing Major lines of Longitude and Latitude
Source: Compiled from the web.
Prime
Meridian
(North –
South lines:
Longitude)
Equator
(East - West
lines:
Latitude)
5

6. •Geographical or
•Spherical
•Projected
•Plane
•Cartesian
Comparison of globe (spheroid) & a flat map of the world. 6

7. Geographic Coordinate Systems
• Reference system for identifying locations and
measuring features on the curved surface of the
earth.
• It consists of a network of intersecting lines called a
graticule or grid
• The graticule is made up of vertical lines, called lines
of longitude (meridians e.g. “Prime Meridian” or
Greenwich Meridian), and horizontal lines, called
lines of latitude (parallels) e.g. Equator
7

8. Projected/Plane/Cartesian Coordinate Systems
• Used to locate objects on a flat surface (either a paper map or a digital
map)
• Projected coordinate systems are based on Cartesian coordinates
(remember the graphs in maths)
• It is a two-dimensional, planar (plane) coordinate system based on a grid in
which x (measures horizontal distance) and y (measures vertical distance)
from an origin
• This same type of spatial reference system is used in making graphs. The x,
y coordinate defines each point in the graticule or grid.
• Points can then be located with respect to the origin and the axes in the
graticule.
8

9. Determination/measurement of Location
or Position on a map
Mathematical location
• With the Rectangular coordinate system, a False Origin is
chosen such the entire earth or the portion of the earth
that is mapped appears on the first quadrant. In such as
case, we have only North and East, no South and West.
• Thus, all coordinates are in East and North
• A False origin is an arbitrary zero point to the south and
west of a grid zone which is assigned to avoid negative
coordinate values.
• The false origin for Ghana is 900,000ft (274,320m,
approx. 300,000m) E, 0ft (0m) N
• At the global level (i.e. UTM), the False origin for the
Northern hemisphere is 500,000m E, 0m N and the
southern hemisphere is 500,000m E, 10,000,000m N False Origin
True Origin

10. Determination of Location or Position
Geographic and Rectangular coordinates on a topomap
Geographic coordinate
mark
Rectangular coordinate
mark

11. Determination of Location
or Position
Geographic and Rectangular
coordinates on a topomap

12. Determination of Location or Position
Steps to determine Mathematical or accurate location on a map
• To measure or determine the coordinates, first determine the point which you will use
to represent the feature. If it is a point feature, then you have no problem, but if it is
an areal feature, you will have to determine an appropriate point. This could be the
town centre, junction, chief’s palace, etc. usually where the town started.
• Next, you locate the grid lines within which the feature falls.
• Draw lines connecting these grids if they are not already on the map. However, be
careful with drawing these lines and clean them afterwards.
• Draw a vertical and horizontal lines through the centre of the point to cut the grid
lines that you just drew.
• N.B: Care must be taken in drawing the lines. If the map is a topo map, then don’t
draw lines on it as your line will obstruct other features. Instead make marks at the
border of the map. Please use set squares to aid in marking.

13. Determination of Location or Position
• Steps to determine Mathematical or accurate location on a map
• Measure the distance between the latitude and the longitude marks in the map with a
rule.
• Measure the distance from the smaller grid value to the point where the line through
the town cuts the gridlines. So you measure from these points to the horizontal and
vertical lines through the town respectively. Note that the lines passing through the
point are the latitude and longitude of the point.
• Find the difference between the latitude grids and the longitude grids
• Use proportions to calculate the latitude difference and the longitude difference.
• Use the formula: Latitude or longitude difference =
(Distance measured from lower grid to horizontal line)/(Distance measured between
grid lines) x Difference between gird values
• Add the answer to the smaller grid value to obtain the latitude of the town.
• Repeat for the longitude

14. Determination of Location or Position
• Place one of the sets square on the line you want to draw. If you want to draw a horizontal line,
place it on the line so that the side follows the line.
• Fix the other set square firmly to it.
• Look at the direction your point and slide the sets squares against each other till you are on the
point (note: when sliding one, the other is firmly fixed. If it moves, then you have to start all over.
• Do same for the other line

15. Determination of Location or Position
• Example: determine the location
of Dormaa Ahenkro on the map
• For Latitude:
• Distance between latitudes (A) =
4.4cm
• Distance between the lower
latitude and latitude passing
through the point (C) = 0.4cm
• Difference between grid latitudes
(Ld) = 7°30’- 7°15’ = 0°15’
• Difference between lower
latitude and latitude passing
through point = (C/A)xLd =
(0.4/4.4)x0°15’ = 0.0909 x 0° 15’ =
0° 1.35’ = 0°01’21”
B
D
A
C

16. Determination of Location or Position
• Latitude of Dorma Ahenkro = 7°15’00” + 0°01’21” = 7°16’21”N
• For longitude:
• Distance between longitudes (B) = 5.8cm
• Distance between the lower longitude and longitude passing through the
point (D) = 3.6cm
• Difference between grid longitudes (Lc) = 3°00’- 2°40’ = 0°20’
• Difference between lower long. and long. passing through point = (D/B)xLc
= (3.6/5.8)x0°20’ = 0.6207 x 0° 20’ = 0°12.414’ = 0°12’25”
• Longitude of Dorma Ahenkro = 2°40’00” + 2°12’25” = 2°52’25”W
• The coordinates of Dorma Ahenkro is latitude 7°16’21”N and longitude
2°52’25”W

17. Plotting a Point on the Map
• Plotting a point is the reverse operation of measuring coordinates on a map
• However some of the steps outlined above are reversed while some remain the
same. So the steps that are reversed are outlined below
• The same formula as above is used
• We know the latitude and longitude of the points but we have to determine the
distances between them and grids so we can measure and plot.
• First the determine the grids within which the point will lie
• Measure the distance between the grids (lower and upper grids) and distance
between the lower grid and point
• Determine the latitude difference from the latitude of the point and the lower grid
latitude
• Substitute the values you have in the formula and calculate the unknown which is
the distance between the lower grid lat.
• Lat. Diff = difference between point and lower grid/diff between grids)x distance
between grids

18. Plotting a Point on the Map
• Measure the distances you just determined from the lower grids on both sides on the map and connect
them.
• Repeat the steps above for the longitude difference
• The intersection of the lines representing the lat. and long should be the location of the point
• Example: locate a point with lat. 7° 22’ 10”N, and long. 2° 39’ 41”W
• This point falls between latitudes 7° 30’ N and 7° 15’ N and longitudes 2° 20’ W and 2° 40’ W.
• lat. difference of grids = 7° 30’ - 7° 15’ = 0° 15’ = 0.25°
• lat. difference of lower grid and point = 7° 22’ 10” - 7° 15’ 0” = 0° 7’ 10” = 0.1194°
• Distance between lat. grids = 4.4cm
• Distance between lower lat. and lat. of point = (0.1194/.25)x4.4cm = 2.1cm
• Do same for the longitude difference
• long. difference of grids = 2° 40’ - 2° 20’ = 0° 20’ = 0.33333°
• long. difference of grids = 2° 39’ 41” - 2° 20’ 0” = 0° 19’ 41” = 0.3281°
• Distance between long. grids = 5.8cm
• Distance between lower long. and long. of point = (0.3281/.3333)x5.8cm = 5.7cm

19. Plotting a Point on the Map
5.7cm
5.7cm
2.1cm
2.1cm
• Measure these distance on
both grids and join them
• Their intersection represents
the location of the point.

20. Uses of Measurements
• Coordinates
1. To locate features on the ground (i.e., features or objects can be traced using their
coordinates)
2. To site projects
3. To determine area of settlements
4. For navigation purposes