**Exercise 3.2 Page: 60**

**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 (â€“3, â€“5).**

**iv. The point identified by the coordinates (2, â€“ 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 isÂ (âˆ’5, 2).

ii. The co-ordinates of C isÂ (5, âˆ’5).

iii. The point identified by the coordinatesÂ (âˆ’3, âˆ’5)Â is E.

iv. The point identified by the coordinatesÂ (2, âˆ’4)Â 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 isÂ (0, 5).

viii. The co-ordinates of the point M isÂ (âˆ’3, 0).

**Exercise 3.3 Page: 651. In which quadrant or on which axis do each of the points (â€“ 2, 4), (3, â€“ 1), (â€“ 1, 0), (1, 2) and (â€“ 3, â€“ 5) lie? Verify your answer by locating them on the Cartesian plane.**

- (â€“ 2, 4): Second Quadrant (II-Quadrant)
- (3, â€“ 1): Fourth Quadrant (IV-Quadrant)
- (â€“ 1, 0): Negative x-axis
- (1, 2): First Quadrant (I-Quadrant)
- (â€“ 3, â€“ 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