Orienting Yourself: The Use of Coordinates | Exercise 1.1

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.

Referring to Fig. 1.3, answer the following questions:

(i) If $\text{D}_1\text{R}_1$ 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 $\text{D}_1$ ?

(iii) If $\text{R}_1$ 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 $\text{B}_1\ (0, 1.5)$ and $\text{B}_2\ (0, 4)$ represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?

Solution

We will use the given coordinates to find distances and compare door widths.

Step 1 — Door's position relative to walls

Let's find the door's distance from the left wall (y-axis). The door $\text{D}_1\text{R}_1$ starts at $\text{D}_1$ . The x-coordinate of $\text{D}_1$ is 8. This is the distance from the y-axis.

$\text{Distance from y-axis} = x_{\text{D}_1}$

$= 8$

$\boxed{8 \text{ units}}$

Let's find the door's distance from the x-axis. The door $\text{D}_1\text{R}_1$ lies on the x-axis. Its y-coordinate is 0.

$\text{Distance from x-axis} = y_{\text{D}_1}$

$= 0$

$\boxed{0 \text{ units}}$

Diagram 1

Step 2 — Coordinates of D1

Let's identify the coordinates of point $\text{D}_1$ . From the figure, $\text{D}_1$ is on the x-axis. Its x-coordinate is 8. Its y-coordinate is 0.

$\text{Coordinates of D}_1 = (x_{\text{D}_1}, y_{\text{D}_1})$

$= (8, 0)$

$\boxed{(8, 0)}$

Diagram 2

Step 3 — Room door width and accessibility

Let's calculate the width of the room door. The door is between $\text{D}_1 (8, 0)$ and $\text{R}_1 (11.5, 0)$ . The width is the difference in x-coordinates.

$\text{Width of room door} = x_{\text{R}_1} - x_{\text{D}_1}$

$= 11.5 - 8$

$\boxed{3.5 \text{ units}}$

Now, let's consider if this width is comfortable. If 1 unit is 1 foot, then 3.5 units is 3.5 feet. This is equal to 42 inches. Standard room doors are typically 30-36 inches wide. So, 42 inches is a comfortable width.

Let's check for wheelchair accessibility. A wheelchair needs at least 32 inches clear width. Since 42 inches is greater than 32 inches, a wheelchair can pass easily. Yes, a person in a wheelchair will be able to enter easily.

Diagram 3

Step 4 — Bathroom door width comparison

Let's calculate the width of the bathroom door. The door is between $\text{B}_1 (0, 1.5)$ and $\text{B}_2 (0, 4)$ . The width is the difference in y-coordinates.

$\text{Width of bathroom door} = y_{\text{B}_2} - y_{\text{B}_1}$

$= 4 - 1.5$

$\boxed{2.5 \text{ units}}$

Now, let's compare it with the room door width. Room door width is 3.5 units. Bathroom door width is 2.5 units. Since 2.5 < 3.5, the bathroom door is narrower.

Diagram 4

Answer

(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 $\text{D}_1$ are (8, 0). (iii) The width of the door is 3.5 units. This is a comfortable width for a room door. Yes, a person in a wheelchair will be able to enter easily. (iv) The bathroom door is narrower than the room door.