Fig. 1.3 shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked Class 9

Fig. 1.3 shows Reiaan’s room with points OABC marking its corners. The x- and y-axes are marked Class 9

Question 1.

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. Class 9

Referring to the given figure, answer the following questions:

i. If D₁ R₁ 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?

Solution:

i. The door is 8 units from the left wall (y-axis). The door is 0 units from the x-axis.

ii. The coordinates of D₁ are (8, 0).

iii. D₁(8, 0) and R₁(11.5, 0)

∴ Width of the door = 11.5 - 8 = 3.5 ft

Yes, this is a comfortable width for the room door.

General width of wheelchair = 2.25 ft

∴ A person in a wheelchair will be able to enter Reiaan's room.

iv. B₁(0,1.5) and B₂(0, 4)

Width of the bathroom door = 4 - 1.5

= 2.5 ft < 3.5 ft

∴ The bathroom door is narrower than the room door.