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CHAPTER 1 STRAIGHT LINESLEARNING OBJECTIVES Upon completion of this chapter, you should be able to do
the following: 1. Calculate the distance between two points. 2. Locate a point by dividing a line segment. 3. Define the inclination of a line and determine the
line's slope. 4. Solve for the slopes of parallel and perpendicular
lines. 5. Compute the angle between two lines. 6. Determine the equation of a straight line using the
pointslope form, the slopeintercept form, and the normal form. 7. Determine the equations of parallel and perpendicular
lines. 8. Calculate the distance from a point to a line. INTRODUCTION The study of straight lines provides an excellent
introduction to analytic geometry. As its name implies, this branch of
mathematics is concerned with geometrical relationships. However, in contrast
to plane and solid geometry, the study of these relationships in analytic
geometry is accomplished by algebraic analysis. The invention of the rectangular coordinate system made
algebraic analysis of geometrical relationships possible. Rene Descartes, a
French mathematician, is credited with this invention; the coordinate system
is often designated as the Cartesian coordinate system in his honor. You
should recall our study of the rectangular coordinate system in Mathematics,
Volume l, NAVEDTRA 10069D1, in which we reviewed the following definitions and
terms: 1.
The values of x along, or parallel to, the X axis are abscissas. They are
positive if measured to the right of the origin; they are negative if measured
to the left of the origin. (See fig. 11.) 2.
The values of y along, or parallel to, the Y axis are ordinates. They are
positive if measured above the origin; they are negative if measured below the
origin. 3.
The abscissa and ordinate of a point are its coordinates. Any
point on the coordinate system is designated by naming its abscissa and
ordinate. For example, the abscissa of point P (fig. 11) is 3 and the ordinate
is  2. Therefore, the symbolic notation for P is
P(3,
2)
Figure 11.Rectangular coordinate system. In
using this symbol to designate a point, the abscissa is always written first,
followed by a comma. The ordinate is written last. The general form of the
symbol is P(x,y) 