To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical. The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate axes.
The horizontal line is called the x - axis, and the vertical line is called the y - axis. The coordinate axes divide the plane into four parts called quadrants. The point of intersection of the axes is called the origin.
The distance of a point from the y - axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the coordinates of the point.
The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis are (0, y). The coordinates of the origin are (0, 0).
The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + denotes a positive real number and – denotes a negative real number.
If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.
Class 10
To locate the position of a point on a plane, you require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate, or abscissa. The distance of a point from the x-axis is called its y-coordinate, or ordinate.
The coordinates of a point on the x-axis are of the form (x, 0), and of a point on the y-axis are of the form (0, y).