Coordinate Questions:

A) When deriving coordinates from a map you can use the same format we used for scale and distance calculations (and simply cross-multiply and divide to answer). 

B) Or you may prefer to just consider this as a task of ‘prorating’.  In another words, you calculate a percent.

A) Using Ratios to 'cross multiply & divide'

A.1) UTM

As an example, assume the UTM grid on your map measures 2 cm between lines and that these lines represent 1000 m on the ground.  Your feature of interest lies between 357,000 and 358,000 m easting (see diagram from NRC).  You measure 0.9 cm from the 357,000 m line.  What is the easting of this point?

Well, it is somewhere between 357,000 and 358,000.  But exactly how far from 357,000 is the point?  Consider what we know:

a) the grid depicts 1,000 m on the ground

b) on the map the grid distance is 2.0 cm

c) the point of interest measures 0.9 cm from 357,000 m

Put this into two ratios:

Now cross-multiply (0.9 cm * 1000m) and divide (by 2 in this case) and get 450 m.

Thus, the easting is 357,000m + 450m = 357,450m

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A.2) Latitude/ Longitude

As an example, let's estimate the longitude of Ottawa from the map provided.  As you can see it lies between 75º and 76º 30' W longitude.  In this example we will determine the longitude to the nearest minute.  (Remember there are 60 minutes in one degree).

From the map we note the following:

a) there is 1.5 degrees or 90 minutes between the lines of longitude on this map

b) the 'map distance' for 90 minutes (i.e. between left & right of map) measures 11.0 cm

c) the 'map distance' from 75 degrees to Ottawa is 5.0 cm

Put this into two ratios:

Now cross-multiply (5.0 cm * 90 sec) and divide (by 11.0 cm in this case) and get 40.9, or 41 minutes.

Thus we get 75º 41' W longitude for Ottawa.

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B) Using Ratios to 'prorate'

As an alternative you can determine the "%" factor.

UTM Example:

If the full distance between the grid lines is 1000m,

then the distance is 45% * 1000m = 450m

Lat/Long Example:

If the full distance is equivalent to 90 minutes,

then the measured distance is 45.5% of a minute.

Expressed in seconds it would be 0.455 * 90 min. = 41 min.