![]() Now, using these distances, how can we describe the points so that there is no confusion? (iv) The perpendicular distance of the point Q from the x - axis measured along the negative direction of the y - axis is OS = RQ = 2 units. (iii) The perpendicular distance of the point Q from the y - axis measured along the negative direction of the x - axis is OR = SQ = 6 units. (ii) The perpendicular distance of the point P from the x - axis measured along the positive direction of the y - axis is PM = O N = 3 units. (i) The perpendicular distance of the point P from the y - axis measured along the positive direction of the x - axis is PN = O M = 4 units. Similarly, we draw perpendiculars QR and QS as shown in Fig. For this, we draw perpendiculars PM on the x - axis and PN on the y - axis. Let us see the distances of the points P and Q from the axes. Consider the following diagram where the axes are drawn on graph paper. ![]() Now, let us see why this system is so basic to mathematics, and how it is useful. So, the plane consisting of the axes and these quadrants is called the as the Cartesian plane, or the coordinate plane, or the x y-plane. These four parts are called the quadrants (one fourth part), numbered I, II, III and IV moving in the anticlockwise direction from O X (see Fig.3.9). You observe that the axes (plural of the word ‘ axis ’) divide the plane into four parts. Similarly, O X ′ and O Y ′ are called the negative directions of the x - axis and the y - axis, respectively. Since the positive numbers lie on the directions O X and O Y, O X and O Y are called the positive directions of the x - axis and the y - axis, respectively. The point where X ′ X and Y ′ Y cross is called the origin, and is denoted by O. The horizontal line X ′ X is called the x - axis and the vertical line Y ′ Y is called the y - axis. Ĭombine both the lines in such a way that the two lines cross each other at their zeroes, or origins (Fig. We do the same thing with Y ′ Y except that Y ′ Y is vertical, not horizontal. Place X ′ X horizontal and write the numbers on it just as written on the number line. These lines are actually obtained as follows : Take two number lines, calling them X ′ X and Y ′ Y. But, when we choose these two lines to locate a point in a plane in this chapter, one line will be horizontal and the other will be vertical, as in Fig. The perpendicular lines may be in any direction such as in Fig.3.6. 3.5.ĭescartes invented the idea of placing two such lines perpendicular to each other on a plane, and locating points on the plane by referring them to these lines. Locations of different numbers on the number line are shown in Fig. The point in the negative direction at a distance r from the origin represents the number minus r. The point in the positive direction at a distance r from the origin represents the number r. If one unit distance represents the number ‘1’, then 3 units distance represents the number ‘3’, ‘0’ being at the origin. We use the number line to represent the numbers by marking points on a line at equal distances. The point from which the distances are marked is called the origin. On the number line, distances from a fixed point are marked in equal units positively in one direction and negatively in the other. ![]() You have studied the number line in the chapter on ‘Number System’. ![]()
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