NCERT Solutions Class 9 Maths Chapter 3- Coordinate Geometry

Coordinate Geometry

Exercise 3.1

Q1. How will you describe the position of a table lamp on your study table to another person?

Answer: We use two lines to describe the position of the table lamp on the study table: a perpendicular and a horizontal line. Consider the table as a plane (x and y axis) with the perpendicular line as the Y axis and the horizontal as the X axis. Take one of the table’s corners as the origin, where the X and Y axes cross. The Y axis now represents the table’s length, while the X axis represents its width. Join the line from the origin to the table light and make a point. The point’s distances from both the X and Y axes should be determined and expressed in terms of coordinates.

Q2. (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 the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 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).

Answer: 

1. There is just one street that may be called that (4,3)

2. There is just one street that may be called that (3,4)

Exercise 3.2

Q1. 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.

Answer: 

1. The x-axis and y-axis are the names given to the horizontal and vertical lines used to calculate the position of any location in the Cartesian plane.

2. Quadrants is the name given to each section of the plane produced by these two lines, the x-axis and the y-axis.

3. The origin is the intersection of these two lines.

Q2. 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 the point L.

8. The coordinates of the point M.

Answer: 

1. B’s coordinates are (-5, 2).

2. C has the coordinates (5, -5).

3. E is the position indicated by the coordinates (-3, -5).

4. G is the location defined by the coordinates (2, -4).

5. Abscissa denotes the point’s x coordinate. As a result, the abscissa of the point D is 6.

6. Ordinate refers to the y coordinate. As a result, the ordinate of point H is -3.

7. The point L’s coordinates are (0, 5).

8. The point M’s coordinates are (-3, 0).

Exercise 3.3

Q1. 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.

Answer: 

(-2, 4) lies in the second quadrant.

(3, -1) lies in the fourth quadrant.

(-1, 0) lies in the negative x axis.

(1, 2) lies in the first quadrant.

(-3, -5) lies in the third quadrant.

Q2. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

Answer :

1.  (-2, 8) – Meeting point of imaginary lines starting 2 units to the left from the origin O and ending 8 units above from the origin O.

2. (-1, 7) – Meeting point of imaginary lines beginning 1 unit to the left from the origin O and ending 7 units above the origin O

3. (0, -1.25) – 1.25 units to the left from origin on the x-axis 

4. (1, 3) – Meeting point of imaginary lines beginning 1 unit to the right from the origin O and, ending 3 units above from the origin O.

5. (3, -1) – intersection of imaginary lines beginning 3 units to the right from the origin O and ending 1 unit below origin O.