Chapter Two Points and Lines

ObjectivesUpon completion of this chapter the student will be able to:

• Define the following terms: point, line, bearing, foreshortened line, oblique line, inclined line, bearing, azimuth, locus, longitude and latitude.

• Determine the equivalent distance in statute miles and feet for a given degree of latitude.

• Determine the equivalent in hours of a given degree of longitude.• Use the AutoCAD commands list, id, and properties to determine

the location of a point.• Describe the difference between a bearing and an azimuth.• Determine the bearing and azimuth of a given line.• Convert from bearings to azimuths and from azimuths to

bearings.• Use AutoCAD to determine the bearing and azimuth of a line.

Introduction to Points and LinesAll objects, whether they are man-made or the result of natural conditions and/or forces, contain points and lines. They are the basic building blocks for all two- and three-dimensional objects. Both points and lines have been widely studied in almost every technical field.

Latitude and Longitude

• This grid network provides worldwide coverage and consists of a system of meridians and parallels known as lines of longitude and latitude.

• Meridians are lines of longitude that run north-south;

• The meridian passing through Greenwich, England, is 0° longitude or the prime meridian.

• Measurements can be made east or west of the prime meridian and range from 0° to 180°.

• Lines of longitude west of the prime meridian are designated by the letter W, or prefaced with a negative (–) sign.

Latitude and Longitude

• Longitude and latitude are measured in degrees, minutes, seconds (DMS).

• Each degree is made up of 60 minutes, and each minute contains 60 seconds.

Latitude and Longitude

Bearings• Angles will vary from 0° to 90°.

• Require a reference plane at the beginning and end.

• Are measured from either a clockwise or counter clockwise direction.

The bearing in the above figure is N60°E

Azimuths• Angles will vary from 0° - 360°.• Require only a numeric value, they are assumed to be referenced from due north unless otherwise

specified.• Are measured only in the clockwise direction.

Converting from Bearing to Azimuths

• For all lines in the first quadrant the angle associated with the bearing will be the same for the azimuth.

• For all lines in the second quadrant the azimuth is calculated by subtracting the bearing from 360°.

• For all lines in the third quadrant the azimuth is calculated by adding the bearing to 180°.

• For all lines in the fourth quadrant the azimuth is calculated by subtracting the bearing from 180°.

Using North as a Reference

Converting from Bearing to Azimuths

• For all lines in the first quadrant the azimuth is calculated by adding the bearing to 180°.

• For all lines in the second quadrant the azimuth is calculated by subtracting the bearing from 180°.

• For all lines in the third quadrant the angle associated with the bearing will be the same for the azimuth.

• For all lines in the fourth quadrant the azimuth is calculated by subtracting the bearing from 360°.

Using South as a Reference

Grade• Is the percentage of inclination between a line and the horizontal

plane. It is defined as the vertical rise of a line divided by its horizontal run with the quotient multiplied by 100

Slope

• Is an angle created between a line and the horizontal plane. It is always measured in degrees.