Coordinate plane
Note:
(i) An ordered pair means two numbers ‘x’ and ‘y’ listed in a specific order such that ‘x’ is placed at the first place and ‘y’ is placed at the second place. We write an ordered pair as (x, y).
(ii) (x, y) is one ordered pair and (y, x) is another ordered pair.
The position of a point in a plane is determined with reference to two fixed mutually perpendicular lines, called the coordinate axes. The horizontal line is called the xaxis and the vertical line is called the yaxis.
Let us note the following points:
(i) The perpendicular distance of a point from the yaxis is called its xcoordinate (or abscissa).
(ii) The perpendicular distance of the point from the xaxis is called its ycoordinate (or its ordinate)
(iii) The abscissa of every point on yaxis is zero.
(iv) The ordinate of every point on the xaxis is zero.
(v) The axes intersect at a point called the origin (i.e. xaxis and yaxis intersect at the origin)
(vi) The coordinates of the origin are (0, 0).
Note:
The positive numbers lie on the directions OX and OY. So OX and OY are positive directions of xaxis and yaxis respectively. Similarly OX' and OY' are called the negative directions of the xaxis and the yaxis respectively.
➢ Quadrants
The coordinate axes divide the plane into four parts called quadrants (onefourth part), numbered I, II, III, and IV anticlockwise from OX.
The coordinates are of the form:
(i) (+, +) in the Iquadrant.
(ii) (–, +) in the IIquadrant.
(iii) (–, –) in the IIIquadrant.
(iv) (+, –) in the IVquadrant.
➢ Plotting a Point in the Plane when Coordinates of the Point are Given
To plot a point in the coordinate plane:
(i) We draw the coordinate axes and choose our units such that we can mark equal distances on the xaxis or on the yaxis or on both axes.
(ii) We take origin as zero on the xaxis as well as on the yaxis.
(iii) The distances marked along OX and OY are taken as positive and those along OX' and OY' are taken as negative.
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