Class 9 Maths Chapter 3 Coordinate Geometry

Exercise 3.1

Question 1.

How will you describe the position of a table lamp on your study table to another person?
Solution:
Consider the lamp as a point P and table as a plane. Choose any two perpendicular edges of the table, say OX and OY. Measure the distance of the lamp i.e., P from the longer edge OX, let it be 30 cm. Again, measure the distance of the lamp P from the shorter edge OY, let it be 20 cm.

Thus, the position of the lamp Preferred to the edges OX and OY is (20,30.)

 Question 2.
(Street Plan): A city has two main roads which cross each other r at the center 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 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 :

1. how many cross-streets can be referred to as (4, 3).
2. how many cross-streets can be referred to as (3, 4).

Solution:

1. here is only one cross-street which can be referred to as (4, 3).
2. There is only one cross-street which can be referred to as (3, 4).

 

 Exercise 3.2

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

1. What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
2. What is the name of each part of the plane formed by these two lines?
3. Write the name of the point where these two lines intersect.

Solution:

1. Horizontal line is known as X-axis and vertical line is known as 7-axis.
2. Each part of the plane formed by horizontal and vertical lines is known as quadrant.
3. Horizontal and vertical lines intersect at the origin.

 Question 2.
See figure, and write the following:

1. The coordinates of B
2. The coordinates of C.
3. The point identified by the coordinates (-3, – 5).
4. The point identified by the coordinates (2, – 4).
5. The abscissa of the point D
6. The ordinate of the point H
7. The coordinates of point L
8. The coordinates of the point M.

Solution:

1. The coordinates of B = (-5,2) and B lies in II quadrant. (∵Abscissa = -5, Ordinate = 2)
2. The coordinates of C = (5, – 5).
3. The point identified by the coordinates (-3, – 5) is
4. The point identified by the coordinates (2, – 4) is
5. The abscissa of the point D =6
6. The ordinate of the point H = -3.
7. The coordinates of the point I = (0, 5). (Lies on Y -axis)
8. The coordinates of the point M = (-3,0). (Lies on X -axis)

Exercise 3.3

 Question 1.
In which quadrant or on which axis does 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.
Solution:

1. (-2, 4) lies in II quadrant.
2. (3,-1) lies in IV quadrant.
3. (-1,0) lies on X-axis.
4. (1, 2) lies in I quadrant.
5. (-3, – 5) lies in III quadrant.

 Question 2.
Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes

Solution:
Let 1 unit = 1 cm, then positions of given points in the Cartesian plane are given below: