NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry - Exercise 3.1

Exercise (3.1)

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

Ans: Consider the figure given below of a study stable, on which a table lamp is placed.

From the Figure, using coordinate geometry concepts,

• Consider the lamp on the table as a point

• Consider the table as a plane 

• When observed from the top the table appears to be rectangular in shape.

• The table has a short edge and a long edge.

• Measure the distance of the lamp from the shorter edge and the longer edge.

Assume that:

Distance of the lamp from the shorter edge is \[15cm\]

Distance of the lamp from the longer edge, its \[25cm\].

Therefore, we can conclude that the position of the lamp on the table can be described in two ways depending on the order of the axes as \[\left( {15,{\rm{ }}25} \right)\] or \[\left( {25,{\rm{ }}15} \right)\].

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 the other streets of the city run parallel to these roads and are \[200{\rm{ }}m\] apart. There are 5 streets in each direction. Using \[1{\rm{ }}cm{\rm{ }} = {\rm{ }}200{\rm{ }}m\], 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 \[\left( {2,{\rm{ }}5} \right)\]. Using this convention, find:

Ans:

• Draw two perpendicular lines as the two main roads of the city that cross each other at the center marking them as N–S and E–W.

• Let us take the scale as \[1{\rm{ }}cm{\rm{ }} = {\rm{ }}200{\rm{ }}m\].

• Draw five streets that are parallel to both the main roads.

Street plan is as shown in the fig.:

(i) How many cross - streets can be referred to as \[\left( {4,{\rm{ }}3} \right)\].

Ans: Only one cross street can be referred to as \[\left( {4,{\rm{ }}3} \right)\].

(ii) How many cross - streets can be referred to as \[\left( {3,4} \right)\]?

Ans: Only one cross street, can be referred to as \[\left( {3,4} \right)\].

Exercise (3.2)

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?

Ans: The names of the horizontal line and vertical line that are drawn to determine the position of any point in the Cartesian plane are called x-axis and y-axis respectively.

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

Ans: The name of each part of the plane that is formed by x-axis and y-axis is called quadrant.

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

Ans: The point, where these lines i.e. x-axis and y- axis intersect is called as origin (O).

2. See the figure, and write the following:

(i) The coordinates of B.

Ans: The coordinates of point B are \[\left( {--5,{\rm{ }}2} \right)\].

(ii) The coordinates of C.

Ans: The coordinates of point C are \[\left( {5,{\rm{ }}--5} \right)\].

(iii) The point identified by the coordinates \[\left( {--3,{\rm{ }}--5} \right)\].

Ans: The point representing the coordinates \[\left( {--3,{\rm{ }}--5} \right)\] is E.

(iv) The point identified by the coordinates \[\left( {2,{\rm{ }}--4} \right)\].

Ans: The point that represents the coordinates \[\left( {2,{\rm{ }}--4} \right)\] is G.

(v) The abscissa of point D.

Ans: The abscissa of point D is 6.

(vi) The ordinate of the point H.

Ans: The abscissa of point H is –3.

(vii) The coordinates of the point L.

Ans: The coordinates of point L are \[\left( {0,{\rm{ }}5} \right)\].

(viii) The coordinates of the point M.

Ans: The coordinates of point M are \[\left( {--3,{\rm{ }}0} \right)\].

Exercise (3.3)

1. In which quadrant or on which axis do each of the points \[\left( {--2,{\rm{ }}4} \right)\], \[\left( {3,{\rm{ }}--1} \right)\], \[\left( {--1,{\rm{ }}0} \right)\], \[\left( {1,{\rm{ }}2} \right)\] and \[\left( {--3,{\rm{ }}--5} \right)\] lie? Verify your answer by locating them on the Cartesian plane.

Ans: To determine the quadrant or axis of the points, plot the points \[\left( {--2,{\rm{ }}4} \right)\], \[\left( {3,{\rm{ }}--1} \right)\], \[\left( {--1,{\rm{ }}0} \right)\], \[\left( {1,{\rm{ }}2} \right)\] and \[\left( {--3,{\rm{ }}--5} \right)\] on the graph

From the above fig., we conclude the following:

• Point \[\left( {--2,{\rm{ }}4} \right)\] lie in 2nd quadrant.

• Point \[\left( {3,{\rm{ }}--1} \right)\] lie in 4th quadrant.

• Point \[\left( {--1,{\rm{ }}0} \right)\] lie on the negative x-axis.

• Point \[\left( {1,{\rm{ }}2} \right)\] lie in 1st quadrant.

• Point \[\left( {--3,{\rm{ }}--5} \right)\] lie in 3rd quadrant.

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

Ans: Using the given table of points

Point A\[\left( {--2,{\rm{ }}8} \right)\], point B \[\left( {--1,{\rm{ }}7} \right)\], point C\[\left( {0,{\rm{ }}--1.25} \right)\], point D\[\left( {1,{\rm{ }}3} \right)\] and point E\[\left( {3,{\rm{ }}--1} \right)\] are plotted as follows:

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry Exercise 3.3

Opting for the NCERT solutions for Ex 3.3 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 3.3 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 9 students who are thorough with all the concepts from the Subject Coordinate Geometry textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 9 Maths Chapter 3 Exercise 3.3 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

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