EN हिं

NCERT Solutions for Class 9th Maths Chapter 1 Exercise Set 1.1 — The 2-d Cartesian Coordinate System

Book page 5 Updated on2026-09-08

Q1.
If D₁R₁ represents the door to Reiaan’s room, how far is the door from the left wall (the y-axis) of the room? How far is the door from the x-axis?
Answer

From Fig. 1.3, the door runs from D₁ (8, 0) to R₁ (11.5, 0) along the bottom wall.

Distance of the door from the left wall (y-axis) = 8 ft at its near end D₁
(the far end R₁ is 11.5 ft from the left wall)
Distance of the door from the x-axis = 0

So the doorway begins 8 ft from the left wall, and it is 0 ft from the x-axis.

Why it happens: The bottom wall of the room is the x-axis in this figure. Every point of the doorway therefore has y-coordinate 0, and the perpendicular distance from the x-axis of a point (x, 0) is 0. The distance from the y-axis is read off the x-coordinate, and along the doorway that x-coordinate runs from 8 to 11.5, so “how far from the left wall” is answered by its nearest edge, 8 ft.
Tip: Whenever a wall has been chosen as an axis, objects standing against that wall get a zero in their coordinates. Choosing the axes well is half the work in a coordinate problem.
Q2.
What are the coordinates of D₁?
Answer

D₁ is the pin on the x-axis at the +8 mark.

D₁ = (8, 0)
Why it happens: D₁ lies on the bottom wall, which is the x-axis, so its y-coordinate must be 0. Counting the unit marks from O along the x-axis gives 8, and the scale is 1 cm : 1 foot, so D₁ is 8 ft to the right of the left wall.
Q3.
If R₁ is the point (11.5, 0), how wide is the door? Do you think this is a comfortable width for the room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily?
Answer

D₁ and R₁ both lie on the x-axis, so the width is just the difference of the x-coordinates.

Width of door = |11.5 − 8| = 3.5 ft
3.5 ft = 3.5 × 12 in = 42 inches ≈ 1.07 m

Yes, this is a comfortable width. Ordinary bedroom doors in India are about 2.5 ft to 3 ft (750–900 mm) wide, so 3.5 ft is generously wide.

Yes, a wheelchair user can enter easily. A standard wheelchair is about 24–26 in across, and barrier-free design guidelines ask for a clear opening of at least 32 in, with 36 in preferred. A 42-inch doorway clears that comfortably, and leaves room for a helper’s hands on the push handles.

Why it happens: The two points differ only in their x-coordinates, so the segment D₁R₁ is parallel to the x-axis and its length is the plain difference |x₂ − x₁|. No square roots are needed — that is the whole point of choosing the wall as an axis.
Check it yourself: Measure the clear opening of a door at home — the gap when the door is fully open, not the outside width of the frame. The door leaf and hinges eat up an inch or two.
Q4.
If B₁ (0, 1.5) and B₂ (0, 4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?
Answer

B₁ and B₂ both lie on the y-axis, so their separation is the difference of the y-coordinates.

Width of bathroom door = |4 − 1.5| = 2.5 ft
Width of room door = 3.5 ft
3.5 − 2.5 = 1

The bathroom door is narrower, by 1 ft.

Why it happens: The bathroom door sits in the left wall, and the left wall is the y-axis. Both ends therefore have x-coordinate 0, the segment is vertical, and its length is |y₂ − y₁|. Notice how the same subtraction idea handles both doors — only the axis changes.
Did you know? 2.5 ft is 30 inches, which is below the 32-inch clear width that barrier-free guidelines ask for. So Reiaan’s room door is wheelchair friendly but his bathroom door is not — a very common problem in Indian homes.
Was this helpful? Report an error