Mapping Reiaan's Room: Exercise Set 1.1
Putting coordinates to work — door widths, wall positions, and what the numbers reveal about a real bedroom
AI Generation Prompt
Ultra-wide cinematic banner (16:5 ratio). A top-down view of a child's bedroom — the same room the student met two pages ago — but now a faint, glowing Cartesian coordinate grid has been laid over it. The corner of the room sits exactly on the origin. The bed, wardrobe, and doors all align cleanly with grid lines. A few key corner points are softly highlighted, suggesting that real, lived spaces become readable as soon as a coordinate system is laid over them. A single warm sunbeam falls across the wooden floor at sunrise. The image conveys: every real space — even something as ordinary as a bedroom — is secretly a coordinate plane waiting to be read. Painterly cinematic illustration with subtle technical overlay. Dark background. No text, no labels.
Suppose I tell you the door of a room starts at the point and ends at the point .
Can you tell me how wide the door is — without ever measuring the door itself?
And if I told you the door of a school classroom is 120 cm wide, can you guess: is the door above wider, or narrower?
Both points have the same y-coordinate, so they are on the same horizontal line. What changes between the two points?
From Bhāskarāchārya's Līlāvatī — the Great Indian Textbook of Practical Mathematics
येषां सुजातिगुणवर्गविभूषितानां
बुद्धिर्न खेदमुपयाति परिश्रमेण।
तेषां सदैव सुखमेव विवर्धते
(yeṣāṃ sujātiguṇavargavibhūṣitānāṃ buddhirna khedam upayāti pariśrameṇa / teṣāṃ sadaiva sukham eva vivardhate)
'जिन लोगों की बुद्धि अच्छे गुणों से सजी होती है — और जो मेहनत से थकते नहीं — उनकी ख़ुशी हमेशा बढ़ती ही जाती है।'
'For those whose minds are adorned with virtue, and who do not tire of effort, happiness only grows.'
Bhāskarāchārya's Līlāvatī, written in 1150 CE, was a textbook of mathematics named after his daughter. It was full of practical problems — measuring fields, calculating doors, dividing wealth — solved in playful Sanskrit verse. The very tradition you are continuing on this page: real spaces, real numbers, real practice. A textbook can be a kind of friendship across centuries.
Reiaan's room on a coordinate grid
Now we put everything you have learned to use.
The diagram below shows Reiaan's room — the same one Shalini built a tactile map for two pages ago — laid out on a Cartesian coordinate grid. The unit on the grid is one foot.
The corners of the room are labelled:
- O = (0, 0) — the bottom-left corner of the room (and the origin of our coordinate system)
- A = (12, 0) — the bottom-right corner, 12 feet along the floor from O
- B = (12, 10) — the top-right corner
- C = (0, 10) — the top-left corner
The left wall of the room sits along the y-axis. The bottom wall sits along the x-axis. So the y-axis is, quite literally, the left wall of Reiaan's room — and the x-axis is the floor's bottom edge as you look down on the floor plan.
Many other points are labelled inside: are the four corners of the wardrobe; are the four corners of the bed; and are the two ends of the room door; and are the two ends of the bathroom door (which sits along the y-axis itself, on the left wall).
We will use these labelled points to answer the questions of Exercise Set 1.1.
AI Generation Prompt
Top-down architectural floor plan of a 12 ft × 10 ft bedroom drawn on a clean Cartesian coordinate grid. Origin O = (0, 0) labelled at the bottom-left corner of the room. Other corners labelled: A = (12, 0) bottom-right, B = (12, 10) top-right, C = (0, 10) top-left. Y-axis runs along the left wall of the room (labelled vertically); x-axis runs along the bottom wall (labelled horizontally). Tick marks at every integer from +1 to +12 on the x-axis and from +1 to +10 on the y-axis, with numbers visible. Inside the room: a bed in the upper-left area with corners labelled S1, S2, S3, S4; a wardrobe (4 ft × 2 ft) on the lower-middle wall with corners W1, W2, W3, W4; a small lamp in the upper-left labelled F. Two doors visible: a bathroom door on the left wall with endpoints labelled B1 (lower) and B2 (upper); a room door on the bottom wall with endpoints labelled D1 (left) and R1 (right). A potted plant in the upper-right corner. Style: clean architectural illustration, hand-drawn warmth with technical precision. Dark background, orange accent labels and grid lines, clean technical illustration style.
Loading simulator…
If represents the door to Reiaan's room, with and :
(a) How far is the door from the left wall (the y-axis) of the room?
(b) How far is the door from the x-axis?
Step 1 — Read off the relevant coordinates.
and . Both points have , so the door lies on the x-axis itself — i.e., flat against the bottom wall of the room.
Step 2 — Distance from the y-axis (left wall).
The x-coordinate of any point measures its horizontal distance from the y-axis. Since the door extends from to , its closest end to the y-axis is , which is 7.5 feet from the y-axis.
Step 3 — Distance from the x-axis.
The y-coordinate measures distance from the x-axis. Both endpoints of the door have , so the door is 0 feet from the x-axis — it sits exactly on it.
Answer:
- The door is 7.5 feet from the left wall (the y-axis).
- The door is 0 feet from the x-axis (it lies on it).
What are the coordinates of ?
Step 1 — Identify the position of on the grid.
is the left end of the room door. From Fig. 1.3, sits on the bottom wall of the room (i.e., on the x-axis), at a horizontal distance of 7.5 feet from the left wall.
Step 2 — Read off both coordinates.
- x-coordinate: 7.5 (distance from the y-axis, on the right side, so positive)
- y-coordinate: 0 (on the x-axis)
Answer: .
If , how wide is the door? Do you think this is a comfortable width for a room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily?
Step 1 — Width of the door.
The door extends from to . Since both points have the same y-coordinate (both lie on the x-axis), the door is a horizontal segment on the bottom wall. Its width is simply the difference in x-coordinates:
In metric units, .
Step 2 — Is this a comfortable width?
Typical residential doors in India are about 30–36 inches (75–90 cm) wide. A 4-foot (122 cm) door is noticeably wider than that — generously sized for a bedroom. So yes, this is a comfortable width.
Step 3 — Wheelchair accessibility.
Indian and international accessibility codes (such as the Harmonised Guidelines for Universal Accessibility, 2021) recommend that doors used by wheelchair users be at least 90 cm (about 3 feet) wide. A 122 cm door is well above this minimum — so a wheelchair user would be able to enter Reiaan's room easily, with room to spare.
Answer: The door is 4 feet (≈ 122 cm) wide — comfortable for everyday use and accessible for wheelchairs.
If and represent the two ends of the bathroom door, is the bathroom door narrower or wider than the room door?
Step 1 — Identify the orientation of the bathroom door.
and . Both points have , so the bathroom door lies along the y-axis itself — i.e., it is a vertical segment on the left wall of the room.
Step 2 — Width of the bathroom door.
Since the door is vertical, its width is the difference in y-coordinates:
In metric units, .
Step 3 — Compare with the room door.
From (iii), the room door is 4 feet wide. The bathroom door is 2.5 feet wide. So:
The bathroom door is narrower than the room door.
A note on accessibility: A 76 cm door is below the 90 cm minimum recommended for wheelchair access. So while Reiaan can enter the room easily through the main door, the bathroom door would be too narrow for a wheelchair to pass through. This is exactly the kind of design oversight that real architects must check for — and exactly what coordinate-based plans help them spot.
Answer: The bathroom door is 2.5 feet wide — narrower than the 4-foot room door.
Imagine that the architect rotates Reiaan's entire floor plan 90° anti-clockwise, so that what was the bottom wall (the x-axis) is now on the left, and what was the left wall (the y-axis) is now on the bottom.
If the architect also relabels the axes so that the new bottom is still called the x-axis and the new left is still called the y-axis — what happens to the coordinates of the room door endpoints and ?
Bridging Science and Society — The Mathematics of Accessibility
Every public building in India built after 2016 is legally required to be accessible to people with disabilities, under the Rights of Persons with Disabilities Act, 2016. Translating that legal requirement into actual buildings is, in part, a problem of coordinate geometry.
What if…
Look around your own home, your school, and the buildings near where you live. Walk through them as if for the first time, paying attention to every door, every step, every ramp.
Q1.A point on the floor plan has coordinates . The unit on the grid is 1 foot. How far is P from the y-axis (the left wall)?
AI Generation Prompt
Ultra-wide cinematic banner (16:5 ratio). A top-down view of a child's bedroom — the same room the student met two pages ago — but now a faint, glowing Cartesian coordinate grid has been laid over it. The corner of the room sits exactly on the origin. The bed, wardrobe, and doors all align cleanly with grid lines. A few key corner points are softly highlighted, suggesting that real, lived spaces become readable as soon as a coordinate system is laid over them. A single warm sunbeam falls across the wooden floor at sunrise. The image conveys: every real space — even something as ordinary as a bedroom — is secretly a coordinate plane waiting to be read. Painterly cinematic illustration with subtle technical overlay. Dark background. No text, no labels.
Suppose I tell you the door of a room starts at the point and ends at the point .
Can you tell me how wide the door is — without ever measuring the door itself?
And if I told you the door of a school classroom is 120 cm wide, can you guess: is the door above wider, or narrower?
Both points have the same y-coordinate, so they are on the same horizontal line. What changes between the two points?
From Bhāskarāchārya's Līlāvatī — the Great Indian Textbook of Practical Mathematics
येषां सुजातिगुणवर्गविभूषितानां
बुद्धिर्न खेदमुपयाति परिश्रमेण।
तेषां सदैव सुखमेव विवर्धते
(yeṣāṃ sujātiguṇavargavibhūṣitānāṃ buddhirna khedam upayāti pariśrameṇa / teṣāṃ sadaiva sukham eva vivardhate)
'जिन लोगों की बुद्धि अच्छे गुणों से सजी होती है — और जो मेहनत से थकते नहीं — उनकी ख़ुशी हमेशा बढ़ती ही जाती है।'
'For those whose minds are adorned with virtue, and who do not tire of effort, happiness only grows.'
Bhāskarāchārya's Līlāvatī, written in 1150 CE, was a textbook of mathematics named after his daughter. It was full of practical problems — measuring fields, calculating doors, dividing wealth — solved in playful Sanskrit verse. The very tradition you are continuing on this page: real spaces, real numbers, real practice. A textbook can be a kind of friendship across centuries.
Reiaan's room on a coordinate grid
Now we put everything you have learned to use.
The diagram below shows Reiaan's room — the same one Shalini built a tactile map for two pages ago — laid out on a Cartesian coordinate grid. The unit on the grid is one foot.
The corners of the room are labelled:
- O = (0, 0) — the bottom-left corner of the room (and the origin of our coordinate system)
- A = (12, 0) — the bottom-right corner, 12 feet along the floor from O
- B = (12, 10) — the top-right corner
- C = (0, 10) — the top-left corner
The left wall of the room sits along the y-axis. The bottom wall sits along the x-axis. So the y-axis is, quite literally, the left wall of Reiaan's room — and the x-axis is the floor's bottom edge as you look down on the floor plan.
Many other points are labelled inside: are the four corners of the wardrobe; are the four corners of the bed; and are the two ends of the room door; and are the two ends of the bathroom door (which sits along the y-axis itself, on the left wall).
We will use these labelled points to answer the questions of Exercise Set 1.1.
AI Generation Prompt
Top-down architectural floor plan of a 12 ft × 10 ft bedroom drawn on a clean Cartesian coordinate grid. Origin O = (0, 0) labelled at the bottom-left corner of the room. Other corners labelled: A = (12, 0) bottom-right, B = (12, 10) top-right, C = (0, 10) top-left. Y-axis runs along the left wall of the room (labelled vertically); x-axis runs along the bottom wall (labelled horizontally). Tick marks at every integer from +1 to +12 on the x-axis and from +1 to +10 on the y-axis, with numbers visible. Inside the room: a bed in the upper-left area with corners labelled S1, S2, S3, S4; a wardrobe (4 ft × 2 ft) on the lower-middle wall with corners W1, W2, W3, W4; a small lamp in the upper-left labelled F. Two doors visible: a bathroom door on the left wall with endpoints labelled B1 (lower) and B2 (upper); a room door on the bottom wall with endpoints labelled D1 (left) and R1 (right). A potted plant in the upper-right corner. Style: clean architectural illustration, hand-drawn warmth with technical precision. Dark background, orange accent labels and grid lines, clean technical illustration style.
Loading simulator…
If represents the door to Reiaan's room, with and :
(a) How far is the door from the left wall (the y-axis) of the room?
(b) How far is the door from the x-axis?
Step 1 — Read off the relevant coordinates.
and . Both points have , so the door lies on the x-axis itself — i.e., flat against the bottom wall of the room.
Step 2 — Distance from the y-axis (left wall).
The x-coordinate of any point measures its horizontal distance from the y-axis. Since the door extends from to , its closest end to the y-axis is , which is 7.5 feet from the y-axis.
Step 3 — Distance from the x-axis.
The y-coordinate measures distance from the x-axis. Both endpoints of the door have , so the door is 0 feet from the x-axis — it sits exactly on it.
Answer:
- The door is 7.5 feet from the left wall (the y-axis).
- The door is 0 feet from the x-axis (it lies on it).
What are the coordinates of ?
Step 1 — Identify the position of on the grid.
is the left end of the room door. From Fig. 1.3, sits on the bottom wall of the room (i.e., on the x-axis), at a horizontal distance of 7.5 feet from the left wall.
Step 2 — Read off both coordinates.
- x-coordinate: 7.5 (distance from the y-axis, on the right side, so positive)
- y-coordinate: 0 (on the x-axis)
Answer: .
If , how wide is the door? Do you think this is a comfortable width for a room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily?
Step 1 — Width of the door.
The door extends from to . Since both points have the same y-coordinate (both lie on the x-axis), the door is a horizontal segment on the bottom wall. Its width is simply the difference in x-coordinates:
In metric units, .
Step 2 — Is this a comfortable width?
Typical residential doors in India are about 30–36 inches (75–90 cm) wide. A 4-foot (122 cm) door is noticeably wider than that — generously sized for a bedroom. So yes, this is a comfortable width.
Step 3 — Wheelchair accessibility.
Indian and international accessibility codes (such as the Harmonised Guidelines for Universal Accessibility, 2021) recommend that doors used by wheelchair users be at least 90 cm (about 3 feet) wide. A 122 cm door is well above this minimum — so a wheelchair user would be able to enter Reiaan's room easily, with room to spare.
Answer: The door is 4 feet (≈ 122 cm) wide — comfortable for everyday use and accessible for wheelchairs.
If and represent the two ends of the bathroom door, is the bathroom door narrower or wider than the room door?
Step 1 — Identify the orientation of the bathroom door.
and . Both points have , so the bathroom door lies along the y-axis itself — i.e., it is a vertical segment on the left wall of the room.
Step 2 — Width of the bathroom door.
Since the door is vertical, its width is the difference in y-coordinates:
In metric units, .
Step 3 — Compare with the room door.
From (iii), the room door is 4 feet wide. The bathroom door is 2.5 feet wide. So:
The bathroom door is narrower than the room door.
A note on accessibility: A 76 cm door is below the 90 cm minimum recommended for wheelchair access. So while Reiaan can enter the room easily through the main door, the bathroom door would be too narrow for a wheelchair to pass through. This is exactly the kind of design oversight that real architects must check for — and exactly what coordinate-based plans help them spot.
Answer: The bathroom door is 2.5 feet wide — narrower than the 4-foot room door.
Imagine that the architect rotates Reiaan's entire floor plan 90° anti-clockwise, so that what was the bottom wall (the x-axis) is now on the left, and what was the left wall (the y-axis) is now on the bottom.
If the architect also relabels the axes so that the new bottom is still called the x-axis and the new left is still called the y-axis — what happens to the coordinates of the room door endpoints and ?
Bridging Science and Society — The Mathematics of Accessibility
Every public building in India built after 2016 is legally required to be accessible to people with disabilities, under the Rights of Persons with Disabilities Act, 2016. Translating that legal requirement into actual buildings is, in part, a problem of coordinate geometry.
What if…
Look around your own home, your school, and the buildings near where you live. Walk through them as if for the first time, paying attention to every door, every step, every ramp.
Q1.A point on the floor plan has coordinates . The unit on the grid is 1 foot. How far is P from the y-axis (the left wall)?