NCERT solution for class 9 maths coordinate geometry ( Chapter 3)

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Solution for Exercise 3.1

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

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Answer :

Let us consider the lamp as a point A and table as a plane.
Take any two perpendicular edges of the table. Measure the distance of the lamp from the longer edge AD (denoting y-axis), let it be 25 cm.
lamp pic
Again, measure the distance of the lamp from the shorter edge AB (denoting x-axis);
let it be 15 cm. Therefore, the position of the lamp can be written as (15, 25).

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 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).

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Answer :

The street plan is shown by the following figure.
lamp pic
(i) There is only one cross-street which could be referred to as (4, 3).

(ii) There is only one cross-street which could be referred to as (3, 4).

Solution for 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?
(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.

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Answer :

(i) Horizontal line is known as x-axis (abscissa) and vertical lane is known as y-axis (ordinate) which are drawn to determine the position of any point in the cartesian plane.

(ii) Each part of the plane formed by horizontal and vertical lines is known as quadrant.

(iii) The point at which these two horizontal and vertical lines intersect is called as origin.

2.See figure, and write the following:
image
(i) The coordinates of B
(ii) The coordinates of c.
(iii) The point identified by the coordinates (-3, — 5).
(iv) The point identified by the coordinates (2, 14).
(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.

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Answer :

(i) The coordinates of B = (-5, 2) and B lies in II quadrant.
(Since, abscissa = -5 & ordinate = 2)

(ii) The coordinates of C = (5, -5).

(iii) The point identified by the coordinates (-3, -5) is E.

(iv) The point identified by the coordinates (2, -4) is G.

(v) The abscissa of the point D = 6.

(vi) The ordinate of the point H = -3.

(vii) The coordinates of the point L = (0, 5) (Lies on y-axis)

(viii) The coordinates of the point M = (-3, 0) (Lies on x-axis)

Solution for Exercise 3.3

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.

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Answer :

(i) (-2, 4) lies in II quadrant

(ii) (3, -1) lies in IV quadrant

(iii) (-1, 0) lies on the negative x-axis

(iv) (1, 2) lies in I quadrant

(v) (-3, -5) lies in III quadrant
Verification :

image

2. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.
x-2-1013
y87-1.253-1
Points(-2, 8)(-1, 7)(0, -1.25)(1, 3)(3, -1)

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Answer :

Let 1 unit = 1 cm, then positions of given points in the Cartesian plane are given below.

image