Bathroom Geometry & The Dining Room: Exercise Set 1.2 (Part 2)
Fitting fixtures inside a bathroom and a dining table inside a room — every corner is a coordinate, every fit is arithmetic
AI Generation Prompt
Ultra-wide cinematic banner (16:5 ratio). A top-down architect's view of a tile-floored bathroom and an adjacent wood-floored dining room separated by an invisible wall, with a faint Cartesian coordinate grid laid across both spaces. The bathroom on the left is rendered in cool blues with a showering area, toilet, and washbasin visible; the dining room on the right has a dining table at its centre. Soft morning light streams across the cool blue tiles into the warm wooden floor. The image conveys: every fixture, every chair, every corner is a set of two numbers in a single quiet language. Painterly cinematic illustration with subtle technical overlay. Dark background. No text, no labels.
Two questions remain in NCERT Exercise Set 1.2 — and both ask you to fit new objects into spaces you already know. A washbasin into the bathroom. A toilet into a free corner. A whole dining room beyond the bedroom door, complete with its own table.
At this point you have all the tools. Coordinates of corners. Sign rules for quadrants. The trick of reading width and height by subtraction.
What is the smallest thing that can break a perfectly-coordinate-correct layout?
It is not arithmetic. It is something a person walking through the room would notice.
From the Mānasāra — A Treatise on Indian Architecture
प्रत्येकं स्थानं मण्डलैः नियम्यते।
वास्तौ अंशेन अंशेन गणितं प्रयुज्यते॥
(pratyekaṃ sthānaṃ maṇḍalaiḥ niyamyate / vāstau aṃśena aṃśena gaṇitaṃ prayujyate)
'हर जगह को एक मण्डल (ग्रिड) से नियम-बद्ध किया जाता है। घर बनाने में, हर हिस्से के लिए गणित अलग से लगता है।'
'Every space is regulated by a grid. In Vāstu architecture, mathematics is applied unit by unit.'
The Mānasāra is a 6th–8th century CE Sanskrit treatise on temple and house architecture. Its central method is to overlay every site with a square grid (a vāstu-puruṣa-maṇḍala) and compute the location of every element — door, hearth, bedroom, water source — by counting grid cells from a reference point. It is exactly coordinate geometry. Indian architects have been laying out rooms by coordinates for at least 1,400 years.
Question 3: The bathroom — corners and fixtures
NCERT Exercise Set 1.2, Q3. Look at Reiaan's bathroom (Fig. 1.5 on the previous page). The bathroom is a rectangle in the negative-x region of the apartment, sharing the y-axis as its right wall.
Three sub-questions follow.
Question 4: The dining room
NCERT Exercise Set 1.2, Q4. The room door leads from Reiaan's bedroom into the dining room. The dining room is 18 ft long and 15 ft wide, with its long side extending from the bedroom-side corner to point on the y-axis side... wait, let's set it up carefully on the coordinate plane below.
Bridging Science and Society — Vāstu and the Modern Architect
Indian Vāstu Shāstra texts (the Manasara, the Mayamatam, the Brihat Samhita) lay out an entire grammar for designing buildings — temples, palaces, ordinary homes — by overlaying the site with a square grid called the vāstu-puruṣa-maṇḍala (typically or cells) and assigning each cell a function.
Practice Yourself — Apartment Geometry
Cover the worked answers and try these on graph paper:
- Mark off a window seat against the dining room's left wall, centred along the wall. Coordinates of the four corners?
- The dining room has a circular pillar of radius 0.5 ft at its centre. What is the coordinate of the centre? What is the smallest rectangle that contains it?
- A 4-ft chair is placed against the side of the dining table at to . Where do the chair's two ends sit?
- The dining table from Q4(ii) is moved 2 ft to the east. Where are its new corners?
- Compute the area of the dining room minus the table footprint. (Hint: this is just two subtractions.)
Answers: 1. — centred along the left wall (, ). 2. Centre ; bounding rect (1 ft × 1 ft). 3. A 4-ft chair against the south side of the table: e.g. ends at and — sliding the chair under the table edge, anywhere as long as it stays in . 4. Add 2 to every x-coordinate: . 5. Dining-room area sq ft; table footprint sq ft; floor area free sq ft.
Q1.The bathroom occupies the rectangle , . Which of the following points lies inside the bathroom?
AI Generation Prompt
Ultra-wide cinematic banner (16:5 ratio). A top-down architect's view of a tile-floored bathroom and an adjacent wood-floored dining room separated by an invisible wall, with a faint Cartesian coordinate grid laid across both spaces. The bathroom on the left is rendered in cool blues with a showering area, toilet, and washbasin visible; the dining room on the right has a dining table at its centre. Soft morning light streams across the cool blue tiles into the warm wooden floor. The image conveys: every fixture, every chair, every corner is a set of two numbers in a single quiet language. Painterly cinematic illustration with subtle technical overlay. Dark background. No text, no labels.
Two questions remain in NCERT Exercise Set 1.2 — and both ask you to fit new objects into spaces you already know. A washbasin into the bathroom. A toilet into a free corner. A whole dining room beyond the bedroom door, complete with its own table.
At this point you have all the tools. Coordinates of corners. Sign rules for quadrants. The trick of reading width and height by subtraction.
What is the smallest thing that can break a perfectly-coordinate-correct layout?
It is not arithmetic. It is something a person walking through the room would notice.
From the Mānasāra — A Treatise on Indian Architecture
प्रत्येकं स्थानं मण्डलैः नियम्यते।
वास्तौ अंशेन अंशेन गणितं प्रयुज्यते॥
(pratyekaṃ sthānaṃ maṇḍalaiḥ niyamyate / vāstau aṃśena aṃśena gaṇitaṃ prayujyate)
'हर जगह को एक मण्डल (ग्रिड) से नियम-बद्ध किया जाता है। घर बनाने में, हर हिस्से के लिए गणित अलग से लगता है।'
'Every space is regulated by a grid. In Vāstu architecture, mathematics is applied unit by unit.'
The Mānasāra is a 6th–8th century CE Sanskrit treatise on temple and house architecture. Its central method is to overlay every site with a square grid (a vāstu-puruṣa-maṇḍala) and compute the location of every element — door, hearth, bedroom, water source — by counting grid cells from a reference point. It is exactly coordinate geometry. Indian architects have been laying out rooms by coordinates for at least 1,400 years.
Question 3: The bathroom — corners and fixtures
NCERT Exercise Set 1.2, Q3. Look at Reiaan's bathroom (Fig. 1.5 on the previous page). The bathroom is a rectangle in the negative-x region of the apartment, sharing the y-axis as its right wall.
Three sub-questions follow.
Question 4: The dining room
NCERT Exercise Set 1.2, Q4. The room door leads from Reiaan's bedroom into the dining room. The dining room is 18 ft long and 15 ft wide, with its long side extending from the bedroom-side corner to point on the y-axis side... wait, let's set it up carefully on the coordinate plane below.
Bridging Science and Society — Vāstu and the Modern Architect
Indian Vāstu Shāstra texts (the Manasara, the Mayamatam, the Brihat Samhita) lay out an entire grammar for designing buildings — temples, palaces, ordinary homes — by overlaying the site with a square grid called the vāstu-puruṣa-maṇḍala (typically or cells) and assigning each cell a function.
Q1.The bathroom occupies the rectangle , . Which of the following points lies inside the bathroom?