# Chapter – 3: Coordinate Geometry

## Exercise 3.1

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

Solution:

For describing the position of table lamp on the study table, we take two lines, a perpendicular and a horizontal line. Considering the table as a plane(x and y axis) and taking perpendicular line as Y axis and horizontal as X axis respectively. Take one corner of table as origin where both X and Y axes intersect each other. Now, the length of table is Y axis and breadth is X axis. From The origin, join the line to the table lamp and mark a point. The distances of the point from both X and Y axes should be calculated and then should be written in terms of coordinates.

The distance of the point from X- axis and Y- axis is x and y respectively, so the table lamp will be in (x, y) coordinate.

Here, (x, y) = (15, 25)

**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 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).**

**Solution:**

- Only one street can be referred to as (4,3) (as clear from the figure).
- Only one street can be referred to as (3,4) (as we see from the figure).

## 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?**

**(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 name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane is x-axis and y-axis respectively.

(ii) The name of each part of the plane formed by these two lines x-axis and y-axis is quadrants.

(iii) The point where these two lines intersect is called the origin.

**2. See Fig.3.14, 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. The co-ordinates of B is (−5, 2).

ii. The co-ordinates 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. Abscissa means x co-ordinate of point D. So, abscissa of the point D is 6.

vi. Ordinate means y coordinate of point H. So, ordinate of point H is -3.

vii. The co-ordinates of the point L is (0, 5).

viii. The co-ordinates 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.**

Solution:

- (– 2, 4): Second Quadrant (II-Quadrant)
- (3, – 1): Fourth Quadrant (IV-Quadrant)
- (– 1, 0): Negative x-axis
- (1, 2): First Quadrant (I-Quadrant)
- (– 3, – 5): Third Quadrant (III-Quadrant)

**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:

The points to plotted on the (x, y) are:

i. (-2, 8)

ii. (-1, 7)

iii. (0, -1.25)

iv. (1, 3)

v. (3, -1)

On the graph mark X-axis and Y-axis. Mark the meeting point as O.

Now, Let 1 unit = 1 cm

i. (-2, 8): II- Quadrant, Meeting point of the imaginary lines that starts from 2 units to the left of origin O and from 8 units above the origin O

ii. (-1, 7): II- Quadrant, Meeting point of the imaginary lines that starts from 1 units to the left of origin O and from 7 units above the origin O

iii. (0, -1.25): On the x-axis, 1.25 units to the left of origin O

iv. (1, 3): I- Quadrant, Meeting point of the imaginary lines that starts from 1 units to the right of origin O and from 3 units above the origin O

v. (3, -1): IV- Quadrant, Meeting point of the imaginary lines that starts from 3 units to the right of origin O and from 1 units below the origin O

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