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SEBA Class 9 Mathematics Chapter 3 Coordinate Geometry
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Coordinate Geometry
Chapter – 3
| Exercise 3.1 |
1. How will you describe the position of a table lamp on your study table to another person?
Ans:
Consider the lamp placed on the table. Take the space taken by the lamp as a point and draw perpendiculars on length AB and breadth BC of the table. Now measure the dis-tance. Let the length of perpen-dicular be 20 cm and 30 cm from length AB and breadth BC respectively. So, the position of the lamp from (AB, BC) edges will be (20, 30).
2. (Street Plan): A city has two main roads meeting at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to main roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw the model of the city on your notebook. Represent roads/streets by single lines.
There are many cross streets in our modal. A particular cross-street is made by two streets, one running in the North-South direction and an-other in the East-West di-rection. Each cross street is referred of in the fol-lowing 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). Us-ing 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)?
Ans: According to question street plan drawn as both the cross streets are marked in the above figure. They are only one found because of the two reference lines we have used for locating them.
| 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?
Ans: The name of horizontal lines drawn to determine the position of any point in the cartesian plane is x-axis.
The name of the vertical line is y-axis.
(ii) What is the name of each part of the plane formed by these two lines?
Ans: The name of each part of the plane formed by x-axis and y-axis is called quadrants (one fourth part) numbered I, II, III and IV anti clock from OX.
(iii) Write the name of the point where these two lines intersect.
Ans: The name of the point where these two lines intersect is origin.
2. See fig 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.
(viii) The coordinates of the point M.
Ans: According to.
(i) The coordinates of B is (-5, 2).
(ii) The coordinates of C is (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 point D is 6.
(vi) The ordinates of the point H is -3.
(vii) The coordinate of the point L is (0, 5)
(viii) The coordinate of the point M is (-3, 0)
| Exercise 3.3 |
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.
Ans:
The point (-2, 4) lies on the IIⁿᵈ quadrant in cartesian plane because in point (-2, 4), x negative and y is positive. Again, the point (3, -1) lie on IVᵗʰ quadrant in cartesian plane because in point (3,-1), x is positive y is negative. Again, the points (1, 0) lie on the x-axis because in point (-1, 0) the value of y is zero.
Again the point (1, 2) lie on 1ˢᵗ quadrant because in point (1, 2) both x and y are positive. The point ( – 3 ,- 5) lies on the III quadrant in the cartesian plane because in point (-3, -5) both x and y are negative.
2. Plot the point (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.
| X | -2 | -1 | 0 | 1 | 3 |
| Y | 8 | 7 | -1.25 | 3 | -1 |
Ans:
The pairs of numbers given in the table can be represented by the points (- 2,8), (-1, 7), (0, -1.25), (1, 3) and (3, -1) we use the scale 1 cm = 1 unit on the axes.
