Planning a room with coordinates

Fig. 1.5 adds Reiaan's bathroom to the left of his room. Because it is left of the y-axis, its points have negative x-coordinates. Mark the x-axis from –7 to 13 and the y-axis from –15 to 12, at 1 cm to 1 unit.

The bathroom is the rectangle O (0, 0), F (0, 9), R (–6, 9), P (–6, 0): 6 ft by 9 ft, as Fig. 1.1 said.

Inside it, the showering area SHWR has corners S (–6, 6), H (–3, 6), W (–2, 9), R (–6, 9). SH and RW are both flat (horizontal), so they are parallel, but SH is 3 ft and RW is 4 ft. One pair of parallel sides makes it a trapezium.

The fourth corner of a rectangle. A rectangle's corners line up in pairs, so each corner takes its x from one neighbour and its y from the other. If three feet of a table are at (8, 9), (11, 9) and (11, 7), the fourth shares its x with (8, 9) and its y with (11, 7): (8, 7).

That table is 11 – 8 = 3 ft long and 9 – 7 = 2 ft wide. Its height can't be found: a floor plan has no height.

Reiaan's door opens from the dining room, 18 ft long from P (–6, 0) to A (12, 0) and 15 ft wide. It lies below the x-axis, with corners P (–6, 0), A (12, 0), (12, –15) and (–6, –15). Its centre is halfway each way: (3, –7.5).