Engineering Calculus Notes 14

Engineering Calculus Notes 14 - 2 CHAPTER 1. COORDINATES...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
2 CHAPTER 1. COORDINATES AND VECTORS P O y x Figure 1.1: Rectangular Coordinates from O lying along our axes (see Figure 1.1 ): thus, one of the vertices between O and P is a point on the x -axis, corresponding to a number x called the abcissa of P ; the other lies on the y -axis, and corresponds to the ordinate y of P . We then say that the (rectangular or Cartesian) coordinates of P are the two numbers ( x,y ). Note that the ordinate ( resp . abcissa) of a point on the x -axis ( resp . y -axis) is zero, so the point on the x -axis ( resp . y -axis) corresponding to the number x R ( resp . y R ) has coordinates ( x, 0) ( resp . (0 ,y )). The correspondence between points of the plane and pairs of real numbers, as their coordinates, is one-to-one (distinct points correspond to distinct pairs of numbers, and vice-versa), and onto (every point P in the plane corresponds to some pair of numbers ( x,y ), and conversely every pair of numbers ( x,y ) represents the coordinates of some point
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online