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Engineering Calculus Notes 14

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

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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 P in the plane). It will prove convenient to ignore the distinction between pairs of numbers and points in the plane: we adopt the notation
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