Q1. Fig. 1.3 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 Fig. 1.3, answer the following questions: 
(i) 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?
(ii) What are the coordinates of D1? 
(iii) 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?
(iv) 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:

From Fig. 1.3:

(i) Distance of the door from the left wall (y-axis) and the x-axis

The room door is represented by D₁R₁.
D₁ = (8, 0) and R₁ = (11.5, 0)
Since the door lies on the x-axis, its distance from the x-axis is 0 units.
The door starts at x = 8, so it is 8 units away from the left wall (y-axis).
Therefore,
Distance from the left wall (y-axis) = 8 units
Distance from the x-axis = 0 units

(ii) Coordinates of D₁:

From the figure, D₁ is located at x = 8 on the x-axis
Therefore, D₁=(8,0)

(iii) Width of the Door:

The width of the door is the difference in x-coordinates between R₁ and D₁,

 R₁ ​=(11.5,0), D₁​=(8,0)

Width = 11.5 - 8 = 3.5 units

 A width of 3.5 units is quite comfortable for a room door. A standard wheelchair is about 2.5 feet (30 inches) wide, so a person in a wheelchair will be able to enter through this door easily.

(iv) Comparing the bathroom door and the room door:

The width of the bathroom door is the difference in y-coordinates between B2 and B1

 Given  B1​=(0,1.5), B2​=(0,4)

Width =4-1.5=2.5 units

From the previous calculations,

the width of the room door =3.5 units

Since 2.5<3.5, the bathroom door is narrower than the room door.