 To locate the position of an object two perpendicular lines are needed:
b. Vertical line
The next section is about the Cartesian system.
 Plane is called the cartesian or coordinate plane.
 Lines in the plane are called the coordinate axes.
 Horizontal line: xaxis
 Vertical line: yaxis
 The distance of a point from the yaxis measured along the xaxis is called its x  coordinate or abscissa.
 The distance of the point from xaxis measured along the yaxis is called its y  coordinate or ordinate.
 The coordinates of the origin are (0,0).
 A point in the first quadrant will have positive abscissa and positive ordinate (+,+)
 A point in the second quadrant will have negative abscissa and positive ordinate (−, +)
 A point in the third quadrant will have negative abscissa and negative ordinate (−, −)
 A point in the fourth quadrant will have positive abscissa and negative ordinate (+, −)
After this topic Plotting a point in the plane if its coordinates are given is discussed.
 If x $\ne $ y, then the position of (x, y) in the cartesian plane is different from the position of (y, x).
The last exercise is 3.3 comprising of 2 questions. In the first question, students have to determine the quadrant of given points and locate the same on the cartesian plane. In the second question, students have to plot the given points on the plane.
After that summary of the chapter is given.
Page No 53:
Question 1:
How will you describe the position of a table lamp on your study table to another person?
Answer:
Consider that the lamp is placed on the table. Choose two adjacent edges, DC and AD. Then, draw perpendiculars on the edges DC and AD from the position of lamp and measure the lengths of these perpendiculars. Let the length of these perpendiculars be 30 cm and 20 cm respectively. Now, the position of the lamp from the left edge (AD) is 20 cm and from the lower edge (DC) is 30 cm. This can also be written as (20, 30), where 20 represents the perpendicular distance of the lamp from edge AD and 30 represents the perpendicular distance of the lamp from edge DC.
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NCERT Solution for Class 9 math  number systems 53 , Question 1
Page No 53:
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 NorthSouth direction and EastWest 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 = 100 m, draw a model of the city on your notebook Represent the roads/streets by single lines.
There are many crossstreets in your model. A particular crossstreet is made by two streets, one running in the NorthSouth direction and another in the EastWest direction. Each cross street is referred to in the following manner: If the 2^{nd} street running in the NorthSouth direction and 5^{th} in the EastWest direction meet at some crossing, then we will call this crossstreet (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:
Both the crossstreets are marked in the above figure. It can be observed that there is only one crossstreet which can be referred as (4, 3), and again, only one which can be referred as (3, 4).
Video Solution for number systems (Page: 53 , Q.No.: 2)
NCERT Solution for Class 9 math  number systems 53 , Question 2
Page No 60:
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?
(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.
Answer:
(i) The name of horizontal lines and vertical lines drawn to determine the position of any point in the Cartesian plane is xaxis and yaxis respectively.
(ii) The name of each part of the plane formed by these two lines, xaxis and yaxis, is quadrant (onefourth part).
(iii) The name of the point where these two lines intersect is the origin.
Video Solution for number systems (Page: 60 , Q.No.: 1)
NCERT Solution for Class 9 math  number systems 60 , Question 1
Page No 60:
Question 2:
See the given figure, and write the following:
(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point identified by the coordinates.
(iv) The point identified by the coordinates
(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
Answer:
(i) The xcoordinate and the ycoordinate of point B are −5 and 2 respectively. Therefore, the coordinates of point B are (−5, 2).
(ii) The xcoordinate and the ycoordinate of point C are 5 and −5 respectively. Therefore, the coordinates of point C are (5, −5).
(iii) The point whose xcoordinate and ycoordinate are −3 and −5 respectively is point E.
(iv) The point whose xcoordinate and ycoordinate are 2 and −4 respectively is point G.
(v) The xcoordinate of point D is 6. Therefore, the abscissa of point D is 6.
(vi) The ycoordinate of point H is −3. Therefore, the ordinate of point H is −3.
(vii) The xcoordinate and the ycoordinate of point L are 0 and 5 respectively. Therefore, the coordinates of point L are (0, 5).
(viii) The xcoordinate and the ycoordinate of point M are −3 and 0 respectively. Therefore, the coordinates of point M is (−3, 0).
Video Solution for number systems (Page: 60 , Q.No.: 2)
NCERT Solution for Class 9 math  number systems 60 , Question 2
Page No 65:
Question 1:
In which quadrant or on which axis do each of the points and lie? Verify your answer by locating them on the Cartesian plane.
Answer:
The point lies in the II^{nd }quadrant in the Cartesian plane because for point, xcoordinate is negative and ycoordinate is positive.
Again, the point lies in the IV^{th} quadrant in the Cartesian plane because for point, xcoordinate is positive and ycoordinate is negative.
The point lies on negative xaxis because for point , the value of ycoordinate is zero and the value of xcoordinate is negative.
The point lies in the I^{st} quadrant as for point , both x and y are positive.
The point lies in the III^{rd} quadrant in the Cartesian plane because for point , both x and y are negative.
Video Solution for number systems (Page: 65 , Q.No.: 1)
NCERT Solution for Class 9 math  number systems 65 , Question 1
Page No 65:
Question 2:
Plot the point (x, y) given in the following table on the plane, choosing suitable units of distance on the axis.

x
− 2
− 1
0
1
3
y
8
7
−1.25
3
− 1
Answer:
The given points can be plotted on the Cartesian plane as follows.
Video Solution for number systems (Page: 65 , Q.No.: 2)
NCERT Solution for Class 9 math  number systems 65 , Question 2
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