Gujarat Board Textbook Solutions Class 9 Maths Chapter 3 Coordinate Geometry
GSEB Solutions Class 9 Maths Chapter 3 Coordinate Geometry
Ex 3.1
Question 1.
How will you describe the position of a table lamp on your study table to another person?
Solution:
Consider ABCD is the surface of table. Choose two adjacent edges AD and DC, i.e., AD as x-axis and DC as y-axis. Let lamp pot be placed at point L whose perpendicular distance from AB i.e., y axis is PL = AQ = 20 cm. Hence abscissa is equal to 20 and the perpendicular distance of L from AD is QL = AP 15 cm, therefore ordinate is equal to 15. Hence the coordinates of point L are (20, 15).
Question 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 m apart. There are 5 streets in each direction. Using 1 cm = 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 North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the second 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).
Solution:
Both the cross-streets are shown in the figure.
We observed that only one cross street which can he referred as (4, 3) and again, only one which can be referred as (3, 4).
Ex 3.2
Question 1.
Write the answer of each of the following questions.
- What is the name of the horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?
- What is the name of each part of the plane formed by these two lines?
- Write the name of the point where these two lines intersect.
Solution:
- The horizontal line is x-axis and the vertical line is the y-axis.
- Quadrants
- The origin
Question 2.
See figure and write the following:
(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, -4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H.
(vii) The coordinates of the point L.
(ix) The coordinates of the point M.
Solution:
(i) B (-5, 2) (ii) C (5, -5)
(iii) E (iv) G
(v) 6 (vi) -3
(vii) L (0, 5) (viii) M (-3, 0)
Ex 3.3
Question 1.
In which quadrant or on which axis do 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.
Solution:
The point (-2, 4) lies in the II quadrant.
The point (3, -1) lies in the IV quadrant.
The point (-1, 0) lies on negative x-axis.
The point (1, 2) lies in the I quadrant.
The point (-3, -5) lies in the III quadrant.
Question 2.
Plot the points (x,y) given in the following table on the plane choosing suitable units of distance on the axes.
Solution: