# 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).