JKBOSE 9th Class Mathematics Solutions Chapter 5 Co-Ordinate Geometry

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Jammu & Kashmir State Board JKBOSE 9th Class Mathematics Solutions

J&K class 9th Mathematics Co-Ordinate Geometry Textbook Questions and Answers

INTRODUCTION

Coordinate geometry is the important branch of Mathematics. The study about it was initially developed by the French philosopher and mathematician Rene Descartes. He described the position of a point in a plane. His method was a development of the older idea of latitude and longitude. The system used for describing the position of a point in a plane is known as cartesian system.

In this chapter you will learn some basic concepts of coordinate geometry.

Rene Descartes (1596 – 1650)

TEXT BOOK EXERCISE – 5.1

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

Ans.— Consider the lamp as a point and table as a plane. Choose any two perpendicular edges of the table. Measure the distance of the lamp from the longer edge. Suppose it is 40 cm. Again, measure the distance of the lamp from the shorter edge, and suppose it is 25 cm. You can write the position of the lamp as (40, 25) or (25, 40), depending on the order fixed by you.

Q. 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 NorthSouth 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 = 200 m, draw a model of the city on your notebook. Represent roads/streets by single lines.

There are many cross-streets in your model. A particular crossstreet 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: 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).

Ans.— The street plan is shown in figure given below :

To reach at cross-street referred as (4, 3); we choose 4th street running in the North-South direction and 3rd street running in the East West direction. Then the cross-street referred as (4, 3) is marked by a

dot • ; as shown in the above figure.

Similarly the cross-street referred as (3, 4) is marked by • We observe that both cross streets are uniquely found because of two reference lines

we have used for locating them.

TEXT BOOK EXERCISE – 5.2

Q. 1. Write the answer of each of the following questions :

(i) What is the name of horizontal and 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.

Ans.— (i) Horizontal and vertical lines which divide the plane into four parts are called axes.

Usual name of horizontal line is x-axis.

Usual name of vertical line is y-axis

Ans.— (ii) Each part formed by these two lines (horizontal and vertical lines) is called quadrant.

Ans.— (iii) Point where these two lines intersect is called origin.

Q. 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,

Solution.—(i) To reach at point B; we move 5 units left of origin then 2 units up.

In other words, x-co-ordinate of B is – 5 and y-co-ordinate is 2. Therefore co-ordinates of B are (-5, 2).

(ii) To locate point C; we move 5 units right of the origin then 5 units down. In other words, x coordinate of x is 5 and y coordinate is -5.

Therefore co-ordinates of C are (5,-5).

(iii) Co-ordinates (-3,-5) are identified by the point E.

(iv) Co-ordinates (2, – 4) are identified by the point G.

(v) Co-ordinates of point D are (6, 0) and hence abscissa i.e. x-coordinate of the point D is 6.

(vi) Ordinate i.e. y-co-ordinate of the point H is – 3.

(vii) To reach at the point L; we move 5 units up on vertical line from origin. In other words, x-coordinate of L is 0 and y co-ordinate is 5. Therefore coordinates of L are (0, 5).

(viii) To locate the point M we move 3 units left on horizontal line from the origin. In other words, x-coordinate of M is – 3 and y-coordinate is 0. Therefore coordinates of M are (-3, 0).

TEXT BOOK EXERCISE – 5.3

Q. 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.— We locate the quadrants or axes corresponding to the given points with the help of following :

Now;

In the point (-2, 4); x-co-ordinates is -ve and y-co-ordinate is +ve.

Therefore point (-2, 4) lies in the II quadrant.

In the point (3,-1): x-coordinate is +ve and y-coordinate is -ve.

Therefore point (3, -1) lies in the IV quadrant.

In the point (-1,0), .x-co-ordinate is -ve and y-coordinate is 0.

Therefore point (-1, 0) lies on the negative .x-axis.

In the point (1, 2); x-co-ordinate is +ve and y-co-ordinate is +ve.

Therefore point (1, 2) lies in the I quadrant.

In the point (−3, −5); x-coordinate is -ve and y-coordinate is -ve.

Therefore point (-3, -5) lies in the III quadrant.

Q. 2. Plot the points (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

Solution.— Points given in the table are plotted in the graph as follows :

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JKBOSE 9th Class Mathematics Solutions Chapter 5 Co-Ordinate Geometry