Mathematics NCERT Grade 9, Chapter 3: Coordinate Geometry: How to locate a point on the number line is already discussed. In the first section, an activity related to seating plan is discussed to explain the concept of coordinate plane.
• To locate the position of an object two perpendicular lines are needed:
a. Horizontal line
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: x-axis
• Vertical line: y-axis
• The distance of a point from the y-axis measured along the x-axis is called its - coordinate or abscissa.
• The distance of the point from x-axis measured along the y-axis 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 (+, −)
2 solved examples are given in this section. Exercise 3.2 is a short exercise containing only 2 questions.
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).
This topic is explained by two solved examples.
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.

#### Question 1:

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

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.

##### Video Solution for coordinate geometry (Page: 53 , Q.No.: 1)

NCERT Solution for Class 9 math - coordinate geometry 53 , Question 1

#### 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 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 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).

Both the cross-streets are marked in the above figure. It can be observed that there is only one cross-street which can be referred as (4, 3), and again, only one which can be referred as (3, 4).

##### Video Solution for coordinate geometry (Page: 53 , Q.No.: 2)

NCERT Solution for Class 9 math - coordinate geometry 53 , Question 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?

(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.

(i) The name of horizontal lines and vertical lines drawn to determine the position of any point in the Cartesian plane is x-axis and y-axis respectively.

(ii) The name of each part of the plane formed by these two lines, x-axis and y-axis, is quadrant (one-fourth part).

(iii) The name of the point where these two lines intersect is the origin.

##### Video Solution for coordinate geometry (Page: 60 , Q.No.: 1)

NCERT Solution for Class 9 math - coordinate geometry 60 , Question 1

#### 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

(i) The x-coordinate and the y-coordinate of point B are −5 and 2 respectively. Therefore, the coordinates of point B are (−5, 2).

(ii) The x-coordinate and the y-coordinate of point C are 5 and −5 respectively. Therefore, the coordinates of point C are (5, −5).

(iii) The point whose x-coordinate and y-coordinate are −3 and −5 respectively is point E.

(iv) The point whose x-coordinate and y-coordinate are 2 and −4 respectively is point G.

(v) The x-coordinate of point D is 6. Therefore, the abscissa of point D is 6.

(vi) The y-coordinate of point H is −3. Therefore, the ordinate of point H is −3.

(vii) The x-coordinate and the y-coordinate of point L are 0 and 5 respectively. Therefore, the coordinates of point L are (0, 5).

(viii) The x-coordinate and the y-coordinate of point M are −3 and 0 respectively. Therefore, the coordinates of point M is (−3, 0).

##### Video Solution for coordinate geometry (Page: 60 , Q.No.: 2)

NCERT Solution for Class 9 math - coordinate geometry 60 , Question 2

#### 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.

The point lies in the IInd quadrant in the Cartesian plane because for point, x-coordinate is negative and y-coordinate is positive.

Again, the point lies in the IVth quadrant in the Cartesian plane because for point, x-coordinate is positive and y-coordinate is negative.

The point lies on negative x-axis because for point , the value of y-coordinate is zero and the value of x-coordinate is negative.

The point lies in the Ist quadrant as for point , both x and y are positive.

The point lies in the IIIrd quadrant in the Cartesian plane because for point , both x and y are negative.

##### Video Solution for coordinate geometry (Page: 65 , Q.No.: 1)

NCERT Solution for Class 9 math - coordinate geometry 65 , Question 1

#### 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