![]() ![]() The Cartesian coordinate system (also called the Cartesian plane, or just the plane) is a flat surface (like the cover of a book) that extends forever in all directions. Something that has two dimensions is a surface. Click on "Solve Similar" button to see more examples. The Cartesian coordinate system is the structure we use to graph points in two dimensions. Let's see how our solver generates graph of this equation and similar equations. ![]() In fact, we shall soon see that they are collinear. These points seem to lie on a straight line and we may reasonably guess that they do. Then plot these points in a coordinate plane. For most equations we can plot only a finite number of points exactly and then make a (more or less) educated guess at the other points.įirst we construct a table listing some of the solution pairs The resulting figure in the plane is called the graph of (2). Since the solution set of (2) is a set of real number pairs, we may plot these pairs as points in a coordinate plane. The solution set is the set of all solution pairs. Is a pair of numbers (a,b) such that the substitution x=a, y=b into (2) results in a true numerical statement. Then h intersects X in a point at directed distance (x,y) stand for any expression in the variables x and y. P which are parallel to X and Y, respectively. Choosing some unit of measure on each of the two lines, we mark off positive distances in the positive direction on X and Y and negative distances in the other direction on each line, so that each point on an axis is at a directed distance from the origin O. It is customary to choose the positive directions as indicated by the arrows in Figure 1. Choose a direction from O along X as the positive direction on X and, similarly, choose a positive direction for Y. The coordinates of P are determined in the following way. The number a is the abcissa or first coordinate of P. while b is the ordinate or second coordinate of P. If P is a point and (a,b) is the pair associated with P, then a and b are the coordinates of P. Using the lines X and Y we will associate a number pair with each point in the plane. Let PI be a plane and let X and Y be mutually perpendicular lines in PI intersecting at the point O. ![]()
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