Look at Reiaan’s bathroom.
- (i) What are the coordinates of the four corners O, F, R, and P of the bathroom?
- (ii) What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.
- (iii) Mark off a 3 ft × 2 ft space for the washbasin and a 2 ft × 3 ft space for the toilet. Write the coordinates of the corners of these spaces.
Step-by-step solution
Idea: The bathroom lies to the left of the y-axis, so all its x-coordinates are negative or zero. Read each point by counting grid squares from O: across first, then up.
(i) What are the coordinates of the four corners O, F, R, and P of the bathroom?
- O is the origin, (0, 0). F is on the y-axis at the top of the bathroom wall, 9 units up: F (0, 9).½ mark
- The bathroom is 6 ft wide and lies to the left of the y-axis, so the far wall is at x = −6: R (−6, 9) and P (−6, 0).½ mark
(ii) What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.
- Reading the grid: S (−6, 6), H (−3, 6), W (−2, 9), R (−6, 9).1 mark
- S and H have the same y-coordinate 6, and W and R have the same y-coordinate 9, so SH and RW are both horizontal, hence parallel. SR is vertical, but HW is slanted, so only one pair of sides is parallel. SHWR is a trapezium (with right angles at S and R). Its parallel sides are SH = 3 ft and RW = 4 ft.½ mark
(iii) Mark off a 3 ft × 2 ft space for the washbasin and a 2 ft × 3 ft space for the toilet. Write the coordinates of the corners of these spaces.
- Both fixtures go against the left wall (x = −6), below the shower area (which starts at y = 6), leaving the floor near the door B1B2 free.½ mark
- Washbasin, 3 ft along the wall and 2 ft out from it, in the corner at P: (−6, 0), (−4, 0), (−4, 3), (−6, 3).½ mark
- Toilet, 2 ft along the wall and 3 ft out from it, leaving a 0.5 ft gap above the basin: (−6, 3.5), (−3, 3.5), (−3, 5.5), (−6, 5.5).½ mark
- Other placements are also correct, as long as each space has the right size, lies inside the bathroom and does not overlap the shower area or the other space.
Check: Bathroom: OP = 0 − (−6) = 6 ft and OF = 9 ft, matching 6 ft × 9 ft ✓. Basin: 3 × 2 ✓; toilet: 3 × 2 with the 2 ft along the wall ✓; the toilet’s top (y = 5.5) is below the shower’s edge (y = 6) ✓.
Answer to write in the exam
(i)
O = (0, 0)
F = (0, 9)
R = (−6, 9)
P = (−6, 0)
(ii)
S = (−6, 6), H = (−3, 6), W = (−2, 9), R = (−6, 9)
SH and RW are horizontal (y = 6 and y = 9) ⇒ SH ∥ RW; HW is not vertical, so SR ∦ HW
∴ SHWR is a trapezium (right-angled at S and R).
(iii)
Washbasin (3 ft × 2 ft): (−6, 0), (−4, 0), (−4, 3), (−6, 3)
Toilet (2 ft × 3 ft): (−6, 3.5), (−3, 3.5), (−3, 5.5), (−6, 5.5)
Common mistakes that cost marks
- Writing R as (6, 9) or P as (6, 0). Points to the left of the y-axis have a negative x-coordinate.
- Calling SHWR a rectangle or a parallelogram. Only SH and RW are parallel; the side HW is slanted.
- Placing the toilet so that it overlaps the shower area (above y = 6) or sticks out beyond the wall at x = −6.
How this can come in the exam
The quadrilateral with vertices (−6, 2), (−1, 2), (−3, 5) and (−6, 5) is a
- rectangle
- trapezium
- parallelogram
- square
Show answer
(B) trapezium
The sides at y = 2 and y = 5 are parallel; the side from (−1, 2) to (−3, 5) is slanted, so only one pair is parallel.
A room plan (1 unit = 1 ft) has corners (−8, 0), (0, 0), (0, 7) and (−8, 7). A 2 ft × 4 ft cupboard is placed in the corner at (−8, 7), with its 4 ft side along the top wall. Write the coordinates of the cupboard’s corners.
Show answer
Along the top wall from x = −8 to −4, and 2 ft down from y = 7 to 5 (1 mark). Corners (−8, 7), (−4, 7), (−4, 5), (−8, 5) (1 mark).Try one yourself
The shower area of another bathroom has corners K (−5, 4), L (−2, 4), M (−1, 8) and N (−5, 8). Name its shape and find the lengths of its two parallel sides.
Show answer
KL (y = 4) ∥ NM (y = 8), and LM is slanted, so it is a trapezium. KL = −2 − (−5) = 3, NM = −1 − (−5) = 4 units.
More questions like this
- Other rooms in the house:
- Look at triangle ADM in the figure. Triangle ADM is an acute angled triangle in the first quadrant. How do we find the lengths of its sides AD, DM and MA?
- 1. In moving from A (3, 4) to D (7, 1), what distance has been covered along the x-axis? What about the distance along the y-axis?
2. Can these distances help you find the distance AD? - What if, x1, x2, y1, y2 take negative values? In the figure, triangle AMD is reflected in the y-axis. What are the coordinates of the images of points A, M, and D?
- 1. What has remained the same and what has changed with this reflection?
2. Would these observations be the same if ΔADM is reflected in the x-axis (instead of the y-axis)?