2CHAPTER 1. COORDINATES AND VECTORSPOyxFigure 1.1: Rectangular CoordinatesfromOlying along our axes (see Figure1.1): thus, one of the verticesbetweenOandPis a point on thex-axis, corresponding to a numberxcalled theabcissaofP; the other lies on they-axis, and corresponds totheordinateyofP. We then say that the (rectangular or Cartesian)coordinatesofPare the two numbers (x,y). Note that the ordinate(resp. abcissa) of a point on thex-axis (resp.y-axis) is zero, so the pointon thex-axis (resp.y-axis) corresponding to the numberx∈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, isone-to-one(distinct points correspond to distinctpairs of numbers, and vice-versa), andonto(every pointPin the planecorresponds to some pair of numbers (x,y), and conversely every pair ofnumbers (x,y) represents the coordinates of some pointPin the plane). Itwill prove convenient to ignore the distinction between pairs of numbersand points in the plane: we adopt the notation
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