1. Chapter Two Points and Lines

2. Objectives
Upon 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.

3. Introduction to Points and Lines
All 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.

4. 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.

5. 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.

6. Latitude and Longitude

7. 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

8. 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.

9. Converting from Bearing to Azimuths
Using North as a Reference
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°.

10. Converting from Bearing to Azimuths
Using South as a Reference
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°.

11. 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

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