Ex 1.2 Class 9 Ganita Manjari Chapter 1: Orienting Yourself: The Use of Coordinates

Class 9 Maths Ganita Manjari Chapter 1 Exercise 1.2 Solutions cover the room-map activity from Orienting Yourself: The Use of Coordinates. In this exercise, students use the x-axis, y-axis and coordinate points to place furniture, locate bathroom corners, study door movement and sketch another room on the coordinate plane.

In Ganita Manjari Class 9 Chapter 1 Exercise 1.2, students move beyond simple points on the x-axis and y-axis. They use Fig. 1.5 to place a study table, check whether the bathroom door hits the wardrobe, identify bathroom and shower-area coordinates, and sketch a dining room using given dimensions. These Class 9 Maths Chapter 1 Exercise 1.2 Solutions show how the Cartesian coordinate system Class 9 concept can describe real positions, lengths and spaces in a practical floor plan.

Class 9 Maths Ganita Manjari Chapter 1 Exercise 1.1 Solutions

1. On a graph sheet, mark the x-axis and y-axis and the origin O. Mark points from (– 7, 0) to (13, 0) on the x-axis and from (0, – 15) to (0, 12) on the y-axis. (Use the scale 1 cm = 1 unit.)

1. Place Reiaan’s rectangular study table with three of its feet at the points (8, 9), (11, 9), and (11, 7).
(i)  Where will the fourth foot of the table be?

Answer:

The given three points form three corners of a rectangle:
A = (8, 9)
B = (11, 9)
C = (11, 7)
To complete the rectangle, the fourth point must have:
– same x-coordinate as A → 8
– same y-coordinate as C → 7
Therefore, the fourth foot is at: (8, 7)

(ii)  Is this a good spot for the table?

Answer:

Yes. The table lies inside Reiaan’s room and does not overlap the bed or wardrobe, so it is a suitable spot.

(iii)  What is the width of the table? The length? Can you make out the height of the table?

Answer:

• Horizontal distance:

   

  $$11-8=3\text{ units}$$ 

• Vertical distance:

   

  $$9-7=2\text{ units}$$ 

Therefore, the table is 3 units long and 2 units wide.

$$\boxed{\text{Length}=3\text{ units},\quad \text{Width}=2\text{ units}}$$

The height cannot be determined from this graph because the graph shows only the table's position and dimensions on the floor (a 2D view), not its vertical height.

2. If the bathroom door has a hinge at B₁ and opens into the bedroom, will it hit the wardrobe? Are there any changes you would suggest if the door is made wider?

Answer:

The bathroom door has its hinge at

$B_1=(0,1.5)$

and extends to

$B_2=(0,4)$

. So its length is:

$$4-1.5=2.5\text{ units}$$

When the door opens into the bedroom, it swings around

$B_1$

. The wardrobe starts at

$x=3$

.

Since the door is only 2.5 units long, its outer edge reaches at most

$2.5$

units from

$B_1$

, while the wardrobe begins 3 units away.

Answer:

No, the door will not hit the wardrobe. There is a small gap between the swinging door and the wardrobe.

If the door is made wider, its swinging radius will increase. If it becomes wide enough to reach the wardrobe, it could hit it. Therefore, a suitable change would be to move the wardrobe farther to the right (or redesign the door to open outward) if a wider door is required.

4. Other rooms in the house:
(i)  Reiaan’s room door leads from the dining room which has the length 18 ft and width 15 ft. The dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners.

Answer:

Coordinates of corners:
P = (-6, 0)
A = (12, 0)
B = (12, -15)
C = (-6, -15)

(ii)  Place a rectangular 5 ft × 3 ft dining table precisely in the centre of the dining room. Write down the coordinates of the feet of the table.

Answer:

To place a rectangular

$5\text{ ft} \times 3\text{ ft}$

dining table exactly at the centre of the dining room:

1) Coordinates of the dining room

The dining room corners are:

$$(-6,0),\ (12,0),\ (12,-15),\ (-6,-15)$$

2) Centre of the dining room

The centre is the midpoint of the room:

$$\left(\frac{-6+12}{2},\frac{0+(-15)}{2}\right)=\left(3,-7.5\right)$$

3) Place the table at the centre

Assume the 5 ft side is parallel to the x-axis and the 3 ft side is parallel to the y-axis.

So from the centre

$(3,-7.5)$

:

• Half of 5 ft =
  $2.5$ 
• Half of 3 ft =
  $1.5$ 

Hence the four feet (corners) of the table are:

$$\boxed{(0.5,-6),\ (5.5,-6),\ (5.5,-9),\ (0.5,-9)}$$

Answer:

$$\boxed{(0.5,-6),\ (5.5,-6),\ (5.5,-9),\ (0.5,-9)}$$

If you want, I can also draw the table placement on the coordinate diagram.

Class 9 Maths Ganita Manjari Chapter 1 Exercises:

• Exercise 1.1: Orienting Yourself: The Use of Coordinates
• Chapter 1: Complete Solution: Orienting Yourself: The Use of Coordinates
• End of Chapter Exercises: Orienting Yourself: The Use of Coordinates