Orienting Yourself: The Use of Coordinates Mathematics Ganita Manjari class 9 in English Medium ncert book solutions Exercise Set 1.2

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.) Using Fig. 1.5, answer the given questions.

Q1. 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?
(ii) Is this a good spot for the table?
(iii) What is the width of the table? The length? Can you make out the height of the table?

Solutions: Q1

(i) Given three feet of the table:
(8, 9), (11, 9), (11, 7)

The top of the table is a rectangle shape

So fourth foot will be (8, 7)

(ii) Yes, It is a good spot and right placement for study table.

Because, 

• it is not touching the bed and any wall.
• it is far away from wardrobe.
• And it is near by right wall.

(iii) Length = x direction = 11 − 8 = 3 units (ft)

      Width = y direction = 9 − 7 = 2 units (ft)

👉 Length = 3 ft, Width = 2 ft

Hieght can't be find by 2D graphs. 

Q2. 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?

Solutions: 

Given that hinge is at point B₁ (0, 3) and the door opens into the bedroom.

From the figure, the wardrobe is located approximately between x = 4 to x = 7, which is sufficiently far from the door.

👉 Therefore, the door will not hit the wardrobe.

If the door is made wider, it may create obstruction inside the bedroom (possibly towards the bed area), so it should not be made wider than the available space (about 3 units).

Q3. Look at Reiaan’s bathroom.
(i) What are the coordinates of the four corners O, F, R, and P of the bathroom?
(ii) What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.
(iii) Mark off a 3 ft × 2 ft space for the washbasin and a 2 ft × 3 ft space for the toilet. Write the coordinates of the corners of these spaces.

Solutions: Q3.

(i) the coordinates of the four corners O, F, R, and P of the bathroom are 

👉 O = (0, 0)

👉 P = (–6, 0)

👉 R = (–6, 10)

👉 F = (0, 10)

(ii) Shape of Bathroom is Rectangle.

And coordinates of SHWR are 

👉 S = (–6, 6)

👉 H = (–2, 6)

👉 W = (–2, 10)

👉 R = (–6, 10)

(iii) Washbasin & Toilet

Example placement (inside bathroom):

Washbasin (3 × 2):

• (–6, 0), (–3, 0), (–3, 2), (–6, 2)

Toilet (2 × 3):

• (–3, 0), (–1, 0), (–1, 3), (–3, 3)

Q4. 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 length of the dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners.
(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.

Solutions: Q4. 

(i) Coordinates of Dining Room

Given:

• Length = 18 ft (P to A) → from (–6, 0) to (12, 0) ✔
• Width = 15 ft (downward)

👉 Coordinates:

• P = (–6, 0)
• A = (12, 0)
• New point = (12, –15)
• New point = (–6, –15)

(ii) Dining Table (5 × 3) at centre

Table half dimensions:

• Length = 5 → half = 2.5
• Width = 3 → half = 1.5

👉 Coordinates:

• (3 − 2.5, -7.5 − 1.5) = (0.5, -9)
• (3 + 2.5, -7.5 − 1.5) = (5.5, -9)
• (5.5, -6)
• (0.5, -6)

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