Chapter 3.Coordinate Geometry

Important Points to Remember

1. What are the coordinates of the origin O? It has zero distance from both the

axes so that its abscissa and ordinate are both zero. Therefore, the coordinates of

the origin are (0, 0).

2. the axes (plural of the word‘axis’) divide the plane into four parts. These four

parts are called the quadrants (one fourth part),numbered I, II, III and IV anticlockwise from OX. So, the plane consists of the axes and

these quadrants.

We call the plane, the Cartesianplane, or the coordinate plane, or the xy-plane.

The axes are called the coordinate axes


                             quadrants II(-x,+Y)             quadrantsI (+x,+Y)

 <———————————————–O.———————————->          X-axis

quadrants III (-x,-Y)                                  quadrants IV(+x,-Y)


1. 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.

2. The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate


3. The horizontal line is called the x -axis, and the vertical line is called the y – axis.

4. The coordinate axes divide the plane into four parts called quadrants.

5. The point of intersection of the axes is called the origin.

6. 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.

7. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the coordinates of

the point.

8. 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).

9. The coordinates of the origin are (0, 0).

10. 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.

11. If x ¹ y, then (x, y) ¹ (y, x), and (x, y) = (y, x), if x = y.

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