# Ch - 3 Coordinate Geometry Solutions Class 9th

**Ex 3.1 Class 9 Maths **

**Question 1.****
****How will you describe the position of a table lamp on your study table to another person?**
Solution:
To describe the position of a table lamp placed on the table, let us consider the table lamp as P and the table as a plane.
Now choose two perpendicular edges of the table as the axes OX and OY.
Measure the perpendicular distance ‘a’cm of P (lamp) from OY. Measure the perpendicular distance ‘b’ cm of P (lamp) from OX.
Thus, the position of the table lamp P is described by the ordered pair (a, b).

**Ex 3.1 Class 9 Maths **

Question 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 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 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). Solution: (i) A unique cross street as shown by the point A(4, 3). (ii) A unique cross street as shown by the point B(3,4). The two cross streets are uniquely found because of the two reference lines we have used for locating them.

**Ex 3.2 Class 9 Maths **

**Question 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.**
Solution:
(i) The horizontal line: x – axis and the vertical line: y – axis.
(ii) Each part is called “Quadrant”.
(iii) Origin

**Ex 3.2 Class 9 Maths **

**Question 2****
****See the given 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.****
****(viii) The coordinates of the point M.**

Solution: From the figure, we have (i) The coordinates of B are (-5,2). (ii) The coordinates of C are (5, -5). (iii) The point E is identified by the coordinates (-3,-5). (iv) The point G is identified by the coordinates (2,-4). (v) The abscissa of the point D is 6. (vi) The ordinate of the point H is -3. (vii) The coordinates of the point L are (0,5). (viii) The coordinates of the point M are (-3,0).

**Ex 3.3 Class 9 Maths **

**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) is having negative abscissa and positive ordinate.
∴ (-2,4) lies in the 2nd quadrant.
The point (3, -1) is having positive abscissa and negative ordinate.
∴ (3, -1) lies in the 4th quadrant.
The point (-1, 0) is having negative abscissa and zero ordinate.
∴ The point (-1, 0) lies on the negative x-axis.
The point (1, 2) is having the abscissa as well as ordinate positive.
∴ Point (1,2) lies in the 1st quadrant.
The point (-3, -5) is having the abscissa as well as ordinate negative.
∴ Point (-3, -5) lies in the 3rd quadrant.
These points are plotted in the Cartesian plane as shown in the following figure as A(-2, 4); B(3, -1); C(-l, 0); D(l, 2) and E (-3, -5).

**Ex 3.3 Class 9 Maths **

**Question 2****
****Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.**

Solution: The given points are (-2, 8), (-1, 7), (0, -1.25), (1,3) and (3, -1). To plot these points: (i) We draw X’OX and YOY’ as axes. (ii) We choose suitable units of distance on the axes. (iii) To plot (-2,8), we start from O, take (-2) units on x-axis and then (+8) units on y – axis. We mark the point as A (-2, 8). (iv) To plot (-1,7), we start from O, take (-1) units on x-axis and then (+7) units on the y – axis. We mark the point as B(-1, 7). (v) To plot (0, -1.25), we move along 1.25 units below the x-axis on the y – axis and mark the point as C(0, -1.25). (vi) To plot (1, 3), we take (+1) unit on the x-axis and then (+3) units on the y – axis. We mark the point as D(1, 3). (vii) To plot (3, -1), we take (+3) units on the x-axis and then (-1) unit on the y – axis. We mark the point E(3, -1).