NCERT solution for class 9 maths coordinate geometry ( Chapter 3)
Solution for Exercise 3.1
Open in new tab link
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.
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).
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).
Open in new tab link
Answer :
The street plan is shown by the following figure.
(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
(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.
Open in new tab link
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.
(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.
Open in new tab link
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
Verify your answer by locating them on the Cartesian plane.
Open in new tab link
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 :
| x | -2 | -1 | 0 | 1 | 3 |
|---|---|---|---|---|---|
| y | 8 | 7 | -1.25 | 3 | -1 |
| Points | (-2, 8) | (-1, 7) | (0, -1.25) | (1, 3) | (3, -1) |
Open in new tab link
Answer :
Let 1 unit = 1 cm, then positions of given points in the Cartesian plane are given below.
