Let us examine the figure to understand the layout of the room. Notice that this only shows the map of the floor. Do you see why the position of the windows cannot be marked on this map?
Step-by-step solution
Idea: A floor map is a two-dimensional drawing: every point on it is fixed by two numbers. Anything that needs a third measurement, height above the floor, cannot be shown on it.
- A floor map is the floor seen from directly above. Each point on it is fixed by two measurements only: how far across the room it is and how far along the room it is.½ mark
- Doors reach down to the floor, so the two ends of each door lie on the floor line and can be marked as points (for example the red dots in the figure).
- A window is not on the floor. It is set into a wall, starting some height above the floor (for example 3 ft up) and ending higher still.½ mark
- Height is a third measurement. A flat map of the floor has no direction for “up”, so it cannot show how high a window is.½ mark
- Seen from above, a window only looks like a short line along a wall, exactly like a door. So we could not even tell a window from a door, and its real position (its height on the wall) cannot be marked.½ mark
Check: Ask: does the object touch the floor? The bed, wardrobe and doors do, and all of them appear on the map. The windows do not, and they are the ones missing.
Answer to write in the exam
A floor map shows the floor seen from above: only its length and breadth (2 dimensions).
Windows are fixed in the walls, at a height above the floor.
Height is a third dimension, which a floor map cannot show.
∴ The position of a window cannot be marked on a floor map.
Common mistakes that cost marks
- Saying the windows are “too small” to draw. Size is not the reason; the reason is that windows are above the floor and the map has no height.
- Thinking a window can be marked like a door. A door’s two ends are on the floor; a window’s ends are up on the wall.
- Confusing a floor plan (seen from above) with a picture of a wall (seen from the front), which is where windows are shown.
How this can come in the exam
A floor plan of a classroom is drawn on a grid. Which of these can be located exactly on it by two coordinates?
- The height of the ceiling fan
- A corner of the teacher’s table
- The top edge of a window
- The height of a wall clock
Show answer
(B) A corner of the teacher’s table
A table leg stands on the floor, so its position needs only two measurements. The other three need a height above the floor.
Assertion (A): A light switch fixed on a wall 1.2 m above the floor cannot be fully located on a floor map.
Reason (R): A floor map shows only two dimensions, the length and breadth of the floor.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(A) Both A and R are true, and R is the correct explanation of A.
Both are true, and the missing third dimension (height) in R is exactly why the switch’s position cannot be fully shown.
Try one yourself
Which of these can be shown fully on the floor plan of a room: (a) the four legs of a study table, (b) a shelf fixed 5 ft up a wall, (c) a ceiling fan? Give a reason.
Show answer
Only (a): the legs stand on the floor. For (b) and (c) the plan can show where they are seen from above, but not their height above the floor.
More questions like this
- The figure shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked in the figure. Point O is the origin.
Referring to the figure, answer the following questions: - 1. What are the standard widths for a room door? Look around your home and in school.
2. Are the doors in your school suitable for people in wheelchairs? - So far, we have only considered points on the two coordinate axes. What can you say about the coordinates of points that are not on either axes?
- Copy the figure and mark S and Q in your diagram. Mark any point P in Quadrant I and any point R in Quadrant III, and write down their coordinates.
- 1. What is the x-coordinate of a point on the y-axis?
2. Is there a similar generalisation for a point on the x-axis?
3. Does point Q (y, x) ever coincide with point P (x, y)? Justify your answer.
4. If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true?