Coordinate Geometry

Important Points:

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.

The best example of coordinates in everyday life is use of longitude and latitude on globe. Each unique location on the earth has a unique combination of longitude and latitude. Global positioning system used by radio taxi operators also uses x,y coordinates to find exact location of a vehicle.

Exercise 3.1

Question 1: How will you describe the position of a table lamp on your study table to another person?

Answer: I will say that the table lamp is at a distance of 10 inches from the left side of the table and 6 inches from the front side of the table.

Question 2: (Street Plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.

There are many cross-streets in your model. A particular cross street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross-street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross –street (2, 5). Using this convention, find:

(a) How many cross-streets can be referred to as (4, 3).

Answer: Only one

(b) How many cross-streets can be referred to as (3, 4).

Answer: Only one