# 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*.

* Y-axis*

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

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

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

*Summary*

**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

axes.

**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*.