Class 9 Maths · Ganita Manjari · Exercise Set 1.2

Exercise Set 1.2 Class 9 · Ganita Manjari

📘 Chapter 1 — Coordinate Geometry 📌 Fig. 1.5 — Reiaan’s house layout

📐 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.

1 Reiaan’s Study Table

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?

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:

the same x‑coordinate as A → 8
the same y‑coordinate as C → 7

✅ Therefore, the fourth foot is at: (8, 7)

(ii)

Is this a good spot for the table?

Yes, this is a good spot because:

The table is placed neatly inside the room.
It does not block doors or pathways.
It is positioned near the wall, which is practical for study.

(iii)

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

Width:

Distance between (8, 9) and (11, 9) = 11 − 8 = 3 units

Length:

Distance between (11, 9) and (11, 7) = 9 − 7 = 2 units

Height:

The height of the table cannot be determined from the given diagram because the figure represents only a top view (2D), not vertical dimensions.

Width

3 units

Length

2 units

Height

— not determinable

2 Bathroom Door & Wardrobe

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?

From Fig. 1.5:

B₁ = (0, 1.5)

B₂ = (0, 4)

So, the bathroom door has width:

= 4 – 1.5 = 2.5 units

If the door is hinged at B₁ and opens into the bedroom, it will sweep an arc of radius 2.5 units from B₁.

Now the wardrobe begins at:

W₁ = (3, 0)

W₄ = (3, 2)

The nearest point of the wardrobe from B₁(0, 1.5) is around x = 3, which is farther than the door width 2.5 units.

✅ Therefore, the bathroom door will not hit the wardrobe.

Suggestion if the door is made wider:

If the door becomes much wider, it may come close to or hit the wardrobe.
In that case, the door could be made to open inward into the bathroom, or
the wardrobe could be shifted slightly to the right, or
the door width could be kept limited for comfortable movement.

3 Reiaan’s Bathroom

(i)

What are the coordinates of the four corners O, F, R, and P of the bathroom?

From Fig. 1.5, the coordinates of the four corners O, F, R and P of the bathroom are:

O = (0, 0)

F = (0, 9)

R = (−6, 9)

P = (−6, 0)

(ii)

What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.

From the figure:

S = (−6, 6)

H = (−3, 6)

W = (−2, 9)

R = (−6, 9)

Since one pair of opposite sides is parallel, SHWR is a trapezium.

🔷 Shape of SHWR = Trapezium

(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.

Washbasin space (3 ft × 2 ft):

Take the rectangle near the bottom-left corner of the bathroom.

(−6, 0.5)

(−5, 0.5)

(−5, 2)

(−6, 2)

Toilet space (2 ft × 3 ft):

Take a rectangle above the washbasin.

(−6, 3)

(−4.5, 3)

(−4.5, 4)

(−6, 4)

4 Other Rooms in the House

(i)

Reiaan’s room door leads from the dining room which has 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.

From Fig. 1.5:

P = (−6, 0)

A = (12, 0)

So, the length of PA = 12 – (−6) = 18 ft, which matches the given length.

If the dining room is 15 ft wide and lies below PA, then its upper side is PA and it extends downward 15 units.

Hence the coordinates of four corners are:

P = (−6, 0)

A = (12, 0)

Q = (12, −15)

S = (−6, −15)

📐 The coordinates of the dining room corners are: (−6, 0), (12, 0), (12, −15), (−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.

The dining room extends:

From x = −6 to x = 12
From y = 0 to y = −15

Centre of the dining room:

x‑coordinate of centre = (−6 + 12) / 2 = 3

y‑coordinate of centre = (0 + (−15)) / 2 = −7.5

Now place a 5 ft × 3 ft table at the centre.

Taking length = 5 units along the x‑axis and width = 3 units along the y‑axis:

Half‑length = 2.5 | Half‑width = 1.5

So the coordinates of corners (feet) of the table are:

(3 − 2.5, −7.5 − 1.5) = (0.5, −9)

(3 + 2.5, −7.5 − 1.5) = (5.5, −9)

(3 + 2.5, −7.5 + 1.5) = (5.5, −6)

(3 − 2.5, −7.5 + 1.5) = (0.5, −6)

✅ The coordinates of the four feet of the dining table are: (0.5, −9), (5.5, −9), (5.5, −6), (0.5, −6)

class 9 ganit manjari chapter 1 exercise 1.2 solution

Exercise Set 1.2 Class 9 · Ganita Manjari

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