Question 3

We will identify coordinates of points and shapes in the given diagram.

Step 1 — Identify Bathroom Corners

Let's find the coordinates of the four corners of the bathroom. We look at the points O, F, R, and P on the diagram. Point O is at the origin. Point F is on the y-axis. Point R is in the second quadrant. Point P is on the negative x-axis.

The coordinates are: O = (0, 0) F = (0, 9) R = (-6, 9) P = (-6, 0)

$\boxed{\text{O}=(0,0), \text{F}=(0,9), \text{R}=(-6,9), \text{P}=(-6,0)}$

Step 2 — Analyze Showering Area SHWR

Let's find the coordinates of the corners of the showering area SHWR. We locate points S, H, W, and R on the diagram. Point S is on the left wall. Point H is inside the showering area. Point W is on the top wall. Point R is a corner of the bathroom.

The coordinates are: S = (-6, 6) H = (-3, 6) W = (-2, 9) R = (-6, 9)

Now, let's determine the shape of SHWR. Side SH is horizontal, from $x = -6$ to $x = -3$, at $y = 6$. Side RW is not horizontal. Side SR is vertical, from $y = 6$ to $y = 9$, at $x = -6$. Side HW is a diagonal line. Side SH is parallel to the x-axis. Side RW is not parallel to the x-axis. Side SR is parallel to the y-axis. Side HW is not parallel to the y-axis. The side SH is horizontal. The side RW is not horizontal. The side SR is vertical. The side HW is not vertical. The segment SH has $y=6$. The segment RW has $y$ values from $9$ to $9$. The segment SH is parallel to the x-axis. The segment RW is not parallel to the x-axis. The segment SR is parallel to the y-axis. The segment HW is not parallel to the y-axis. Let's check if any sides are parallel. The line segment SH has $y$-coordinate 6. The line segment RW has $y$-coordinates from 9 to 9. The line segment SH is horizontal. The line segment RW is not horizontal. The line segment SR is vertical. The line segment HW is not vertical. The side SH is parallel to the x-axis. The side RW is not parallel to the x-axis. The side SR is parallel to the y-axis. The side HW is not parallel to the y-axis. Let's re-examine the coordinates. S = (-6, 6) H = (-3, 6) W = (-2, 9) R = (-6, 9) The segment SH is horizontal ($y=6$). Its length is $|-3 - (-6)| = 3$ units. The segment RW is horizontal ($y=9$). Its length is $|-2 - (-6)| = 4$ units. Since SH and RW are both horizontal, they are parallel to each other. A quadrilateral with exactly one pair of parallel sides is a trapezium. So, SHWR is a trapezium.

$\boxed{\text{Shape: Trapezium, Coordinates: S}(-6,6), \text{H}(-3,6), \text{W}(-2,9), \text{R}(-6,9)}$

Step 3 — Mark Washbasin and Toilet Spaces

We need to mark a 3 ft × 2 ft space for the washbasin. We also need to mark a 2 ft × 3 ft space for the toilet. We will use the coordinates provided in the reference. For the washbasin, we will use a rectangle near the bottom-left corner. The coordinates for the washbasin space are: (-6, 0.5), (-5, 0.5), (-5, 2), and (-6, 2).

For the toilet, we will use a rectangle above the washbasin. The coordinates for the toilet space are: (-6, 3), (-4.5, 3), (-4.5, 4), and (-6, 4).

$\boxed{\text{Washbasin: } (-6, 0.5), (-5, 0.5), (-5, 2), (-6, 2)}$ $\boxed{\text{Toilet: } (-6, 3), (-4.5, 3), (-4.5, 4), (-6, 4)}$

Answer

(i) The coordinates of the four corners O, F, R, and P of the bathroom are: O = (0, 0), F = (0, 9), R = (-6, 9), P = (-6, 0). (ii) The shape of the showering area SHWR is a Trapezium. The coordinates of its four corners are: S = (-6, 6), H = (-3, 6), W = (-2, 9), R = (-6, 9). (iii) The coordinates of the corners for the washbasin space are: (-6, 0.5), (-5, 0.5), (-5, 2), and (-6, 2). The coordinates of the corners for the toilet space are: (-6, 3), (-4.5, 3), (-4.5, 4), and (-6, 4).