![]() ![]() The co-ordinate of a point on a plane referred to oblique axes are called oblique co-ordinate. The co-ordinate axes through the origin O are said to be oblique if they are not inclined at right angles. Therefore, the co-ordinate of a point on x-axis are of the form A (x, 0), the co-ordinate of a point on y-axis are of the form B (0, y) and the co-ordinate of the origin O are always (0, 0). Note: That the ordinate of any point on x-axis is zero, abscissa of any point on y-axis is zero and both the abscissa and ordinate of the origin O are zero. Having co-ordinate (x, y) lies in the first quadrant, Having co-ordinate (-x, y) lies in the second quadrant, Having co-ordinate (-x, -y) lies in the third quadrant, Having co-ordinate (x, -y) lies in the fourth quadrant. Conversely, if x,y are real and positive then the point. clearly, abscissa and ordinate are both positive for any point lying in the first quadrant abscissa and ordinate is positive for any point lying in the second quadrant abscissa and ordinate are both negative for any point lying in the third quadrant while the abscissa is positive and ordinate is negative for any point lying in the fourth quadrant. ![]() Here, a is called the abscissa or x co-ordinate of A and b is called the ordinate or y co-ordinate of A. Depending on the signs of a and b the point A may be on the first or second or third of fourth quadrant. In general, the statement, the co-ordinate of a point A are (a, b) means that the point A is situated at distance a units from origin O along x-axis and at distance b units from origin along (or parallel) to y- axis. Thus, the co-ordinate of the points P, Q, R and S are (4, 5), (-4, 5), (-4, -5) and (4, -5) respectively. Therefore, the Cartesian co-ordinate of a point on a plane may be defined as an ordered pair of signed real numbers. These two signed real numbers together are called the rectangular Cartesian co-ordinates of the given point we write the two signed real number in braces putting a comma between them where the first number is the distance from origin along x-axis and the second number is the distance from origin along y-axis (or parallel to y-axis). (ii) the distance measured from O along y-axis in the upward direction (i.e., in the direction OY or in direction parallel to OY) is positive and the distance from y- axis in the downward direction (i.e., in the direction OY’ or in direction parallel to OY’) is negative.īy the above convention of sign the distances along x-axis as well as along y- axis are positive for P, for the point Q, the distance along x-axis is negative and that along x-axis is negative and that along y- axis is positive, for R both these distances are negative and for S the distance along x-axis is positive and that along y is negative.įrom the above discussion it is evident that to determine uniquely the position of a point on a plane referred to mutually perpendicular co-ordinate axes drawn through an origin O we require two signed real numbers. (i) the distance measured from O along x-axis on the right side (i.e., in the direction OX or in direction parallel to OX is positive and the distance from O along x-axis on the left side (i.e., in the direction OX’ or in direction parallel to OX’ is negative To differentiate among the position of such points we introduce the following convention regarding the signs of distances along the co-ordinate axes: Therefore, it is possible to have four different point on the plane of the page at equal distances along the co-ordinate axes. Note that, we shall have points Q, R and S in the second, third and fourth quadrants respectively and the distance of each of them along x-axis and y-axis are 4 and 5 units respectively. If OM and MP measure 4 and 5 units respectively then the position of P on the plane is determined i.e., to get the point P on the plane, we are to move from O through a distance of 4 unite along OX and then to proceed through a distance of 5 units in direction parallel to OY. Let P be any point in the first quadrant. ![]()
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