PSEB Solutions for Class 9 Maths Chapter 3 Coordinate Geometry
PSEB 9th Class Maths Solutions Chapter 3 Coordinate Geometry
Ex 3.1
Question 1.
How will you describe the position of a table lamp on your study table to another person?
Answer:
First of all. I will explain that the study table is the first quadrant of the Cartesian plane, the edge nearer to me as the positive direction of the x-axis and the edge on my left Is the positive direction of the y-axis. Now, I will measure the distance of the table lamp from the edge nearer to me. Suppose that distance is y cm. Now, I will measure the distance of the table lamp from the edge on my left. Suppose that distance is x cm. Now, I can describe the position of the table lamp that it is y cm away from the edge nearer to me and x cm away from the edge on my left. In this manner, I can describe the position of any object lying on the table with two independent informations.
Question 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 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:
Answer:
(i) how many cross-streets can be referred to as (4, 3).
Answer:
One and only one cross-street can be referred to as (4, 3) because it is the intersection of 4th street running in the North-South direction and the 3rd street running in the East-West direction. As we are using two independent references, each cross-street (X, y) will be referred uniquely.
(ii) how many cross-streets can be referred to as (3, 4).
Answer:
One and only one cross-street can be referred to as (3, 4) because it is the intersection of the 3rd street running in the North-South direction and the 4th street running in the East-West direction.
Ex 3.2
Question 1.
Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
Answer:
The horizontal line and the vertical line drawn in the Cartesian plane to determine the position of any point are named as the x-axis and the y-axis respectively.
(ii) What is the name of each part of the plane formed by these two lines?
Answer:
These two lines (x-axis and y-axis) partition the Cartesian plane into four parts each of which is called a quadrant. They are named as Quadrant 1, Quadrant 2, Quadrant 3 and Quadrant 4.
(iii) Write the name of the point where these two lines intersect.
Answer:
These two lines (x-axis and y-axis) intersect at the point named as the Origin.
Question 2.
See the figure given below and write the following:
(i) The coordinates of B.
Answer:
(- 5, 2)
(ii) The coordinates of C.
Answer:
(5, – 5)
(iii) The point identified by the coordinates (-3, -5).
Answer:
E
(iv) The point identified by the coordinates (2, -4).
Answer:
G
(v) The abscissa of the point D.
Answer:
6
(vi) The ordinate of the point H.
Answer:
– 3
(vii) The coordinates of the point L.
Answer:
(0, 5)
(viii) The coordinates of the point M.
Answer:
(- 3, 0)
Ex 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.
Answer:
| Coordinates of the point | Position of the point |
| (- 2, 4) | In the 2nd quadrant |
| (3, – 1) | In the 4th quadrant |
| (- 1, 0) | On the x-axis |
| (1, 2) | In the 1st quadrant |
| (- 3, – 5) | In the 3rd quadrant |
Question 2.
Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes:
Answer:
MCQ
Multiple Choice Questions and Answer
Answer each question by selecting the proper alternative from those given below each question to make the statement true:
Question 1.
For x = 2, y = 3, u = – 2 and v = – 3, point (x + y, u + v) lies in the ……………. quadrant.
A. first
B. second
C. third
D. fourth
Answer:
D. fourth
Question 2.
For x = 4, y = – 5, u = – 6 and v = 8, point (x + y, u + v) lies In the quadrant.
A. first
B. second
C. third
D. fourth
Answer:
B. second
Question 3.
If (x, y) and (y, x) represent the same point in the coordinate plane, then is possible.
A. x = 5, y = 2
B. x = 2, y = 5
C. x = – 5. y = – 2
D. x = 5, y = 5
Answer:
D. x = 5, y = 5
Question 4.
The line Joining P(3, -2) and Q(3, 4)
A. is parallel to the x-axis
B. is parallel to the y-axis
C. is perpendicular to the y-axis
D. intersects both the axes
Answer:
B. is parallel to the y-axis
Question 5.
The line joining A(- 2, 5) and B(- 2, – 8)
A. is parallel to the x-axis
B. is perpendicular to the x-axis
C. intersects the y-axis
D. intersects both the axes
Answer:
B. is perpendicular to the x-axis
Question 6.
The line joining A (- 2, 5) and B (3, 5) intersects ……………….. .
A. the x-axis at (- 2, 0)
B. the x-axis at (3, 0)
C. the y-axis at (0, 5)
D. the x-axis at (5, 0)
Answer:
C. the y-axis at (0, 5)
Question 7.
The line joining A (3, 2) and B (3, – 2) intersects …………………….. .
A. the x-axis at (0, 3)
B. the x-axis at (3, 0)
C. the y-axis at (0, 2)
D. the y-axis at (0, – 2)
Answer:
B. the x-axis at (3, 0)