Question 2

Let's find the door's width and its swing to check for collision.

Step 1 — Calculate door width

First, we find the coordinates of points B1 and B2. From the diagram, B1 is at $x=0$ and $y=1.5$. So, $\text{B}_1 = (0, 1.5)$. From the diagram, B2 is at $x=0$ and $y=4$. So, $\text{B}_2 = (0, 4)$. The bathroom door is between $\text{B}_1$ and $\text{B}_2$. Its width is the distance between these two points.

Bathroom door width:

$= y_{\text{B}_2} - y_{\text{B}_1}$

$= 4 - 1.5$

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

Step 2 — Check for collision

The door is hinged at $\text{B}_1 (0, 1.5)$. It opens into the bedroom. The door will sweep an arc with a radius of 2.5 units. This arc starts from $\text{B}_1$ and moves into the positive x-direction. The farthest point the door can reach is $x = 2.5$ from the hinge. Now, let's look at the wardrobe. The wardrobe starts at $\text{W}_1 (3, 0)$ and $\text{W}_4 (3, 2)$. The nearest x-coordinate of the wardrobe is 3 units. We compare the door's maximum reach with the wardrobe's position.

Door's maximum reach:

$= 2.5 \text{ units}$

Wardrobe's nearest x-position:

$= 3 \text{ units}$

Since $2.5 < 3$, the door will not hit the wardrobe.

Step 3 — Suggest changes for a wider door

If the door is made wider, its swing radius will increase. If the width exceeds 3 units, it will hit the wardrobe. Let's consider some changes.

Answer

(i) No, the bathroom door will not hit the wardrobe. (ii) If the door is made much wider, it may hit the wardrobe. (iii) We could make the door open inwards into the bathroom. Alternatively, the wardrobe could be shifted to the right. Or, the door width could be kept limited for comfortable movement.