TEXTBOOKEXERCISE – 3.1

Some Important Points about Coordinate Geometry

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 it’s 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 is (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 ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.

TEXTBOOKEXERCISE – 3.1

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

Sol. The table lamp is 2 feet from the seating side of the desk and 1 foot from its right edge. So, we can write the position of lampas (2, 1).

Q.2. (Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the 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 :

(i) how many cross-streets can be referred to as (4, 3)?

(ii) how many cross-streets can be referred to as (3, 4)?

Sol. Only one cross-street can be referred to as (4, 3). A different cross-street can refer to as (3, 4). There is only one such cross-street.

TEXTBOOKEXERCISE – 3.2

1. Write the answer to each of the following questions :

(i) What is the name of the horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

(ii) What is the name of each part of the plane formed by these two lines?

(iii) Write the name of the point where these two lines intersect.

Sol. (i) x-axis and y-axis (ii) Quadrants (iii) Origin

2. See Fig. and write the following :

(i) The coordinates of B.

(ii) The coordinates of C.

(iii) The point identified by the coordinates (–3, –5).

(iv) The point identified by the coordinates (2, – 4).

(v) The abscissa of the point D.

(vi) The ordinate of the point H.

(vii) The coordinates of the point L.

(viii) The coordinates of the point M.

Sol. (i) (–5, 2) (ii) (5, –5)

(iii) E (iv) G

(v) 6 (vi) –3

(vii) (0, 5) (viii) (–3, 0)

TEXTBOOKEXERCISE – 3.3

In which quadrant or on which axis do each of the points (–2, 4), (3, – 1), (–1, 0), (1, 2) and (–3, –5) lie? Verify your answer by locating them on the Cartesian plane.