![]() ![]() You could go to any position in the plane, an infinite number of points in the plane, every single one will have a unique ordered pair, a unique x-y coordinate denoting its exact location. Every one of the infinite number of points in the plane can be indicated by a unique ordered pair. First the x-coordinate then the y-coordinate. ![]() As you may remember, 5,4 is an ordered pair, with an x-coordinate followed by a y-coordinate, so they are in alphabetical order. That is the ordered pair that denotes the exact position of that point. It is on the same horizontal line as y equals 4, so its hori, so its y-coordinate is 4, and its position is given by 5,4. This particular point is, the point is vertically above x equals five, so the x coordinate has to be five. So for example, we look at this particular point. Of course, this allows us to indicate the position of any point on the plane by the x and y coordinate of the point. The point where the axes cross, zero on each axis, is called the origin, and that's considered the center of the entire plane. Each one of them contains positive whole numbers, negative whole numbers, positive fractions and decimals, negative fractions and decimals, the whole nine yards. And of course, each one of them goes on forever. The vertical number line is called the y-axis. ![]() The horizontal number line is called the x-axis. And so what we have here really are just two number lines crossing. And it goes on forever in both the positive direction and the negative direction. So of course, we know a number line has whole numbers on it. Descartes' brilliant idea began by simply putting two number lines at right angles to each other. Other names include the x-y plane, the rectangular coordinate plane, and the Cartesian plane, and that final name is in honor of the person who discovered it, the French mathematician Rene Descartes. One of the most elegant ideas in all of mathematics is the idea of the coordinate plane. ![]()
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