In the given figure, Reiaan's room is shown with points $OABC$ marking its corners. The $x$- and $y$-axes are marked in the figure. Point $O$ is the origin.

(A) 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?

(B) What are the coordinates of D₁?

(C) 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?

(D) 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? [Page No. 4]

(A) From the figure, $D_1$ lies on the bottom wall (the $x$-axis) at $x = 8$.

So,

Distance of the door from the $y$-axis (left wall) = 8 ft (the $x$-coordinate of $D_1$).

Distance of the door from the $x$-axis = 0 ft (the door is on the $x$-axis itself).

(B) $D_1$ is on the $x$-axis, i.e., $y = 0$.

From the figure, its $x$-coordinate 8.

Thus, $D_1 = (8, 0)$.

(C) Both $D_1$ and $R_1$ lie on the $x$-axis, so the door width is the difference of $x$-coordinates.

Width of door = ($x$-coordinate of $R_1$) - ($x$-coordinate of $D_1$) = $11.5 - 8 = 3.5$ ft.

A 3.5 ft wide door is quite comfortable, as standard residential doors are usually about 3 ft wide. A wheelchair typically requires a minimum clear width of about 32 inches, though 36 inches is recommended. Since 3.5 ft is well above this minimum width, a person in a wheelchair can enter easily.

(D) Both $B_1$ and $B_2$ lie on the $y$-axis ($x = 0$). The door width is the difference of $y$-coordinates.

Bathroom door width = $4 - 1.5 = 2.5$ ft.

The bathroom door (2.5 ft) is narrower than the room door (3.5 ft).