Look at Reiaan’s bathroom. (i) What are the coordinates of the four corners , , , and of the bathroom? (ii) What is the shape of the showering area in Reiaan’s bathroom? Write the coordinates of the four corners. (iii) Mark off a space for the washbasin and a space for the toilet. Write the coordinates of the corners of these spaces.

Orienting Yourself: The Use of Coordinates | Exercise 1.2

Question 3

Look at Reiaan’s bathroom.

(i) What are the coordinates of the four corners $\text{O}$ , $\text{F}$ , $\text{R}$ , and $\text{P}$ of the bathroom?

(ii) What is the shape of the showering area $\text{SHWR}$ in Reiaan’s bathroom? Write the coordinates of the four corners.

(iii) Mark off a $3\text{ ft} \times 2\text{ ft}$ space for the washbasin and a $2\text{ ft} \times 3\text{ ft}$ space for the toilet. Write the coordinates of the corners of these spaces.

Solution

Understand the Question

A coordinate system uses an ordered pair $(x, y)$ to describe positions on a grid, where $x$ indicates the horizontal distance from the origin (left is negative, right is positive) and $y$ indicates the vertical distance (down is negative, up is positive).
The origin $\text{O}$ has coordinates $(0, 0)$ .
Horizontal line segments share the same $y$ -coordinate, while vertical line segments share the same $x$ -coordinate. A quadrilateral with exactly one pair of parallel opposite sides is a trapezium.

(i) What are the coordinates of the four corners $\text{O}$ , $\text{F}$ , $\text{R}$ , and $\text{P}$ of the bathroom?

Step 1 · Find the Coordinates of the Bathroom Corners

From the grid layout of the bathroom: Diagram 1

$\text{O}$ is at the origin: $(0, 0)$
$\text{F}$ is $9\text{ units}$ along the positive $y$ -axis: $(0, 9)$
$\text{R}$ is at $x = -6$ and $y = 9$ : $(-6, 9)$
$\text{P}$ is $6\text{ units}$ along the negative $x$ -axis: $(-6, 0)$

Answer

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

(ii) What is the shape of the showering area $\text{SHWR}$ in Reiaan’s bathroom? Write the coordinates of the four corners.

Step 1 · Find the Coordinates and Identify the Shape of SHWR

From the grid, locate the four vertices of $\text{SHWR}$ : Diagram 2

$\text{S} = (-6, 6)$
$\text{H} = (-3, 6)$
$\text{W} = (-2, 9)$
$\text{R} = (-6, 9)$

Analyze the opposite sides:

Side $\text{SH}$ lies along the horizontal line $y = 6$ with length: $|-3 - (-6)| = 3\text{ units}$
Side $\text{RW}$ lies along the horizontal line $y = 9$ with length: $|-2 - (-6)| = 4\text{ units}$

Since both $\text{SH}$ and $\text{RW}$ are horizontal lines, they are parallel ( $\text{SH} \parallel \text{RW}$ ). The non-parallel sides $\text{SR}$ (vertical) and $\text{HW}$ (slanted) are not parallel.

Therefore, quadrilateral $\text{SHWR}$ is a trapezium.

Answer

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

(iii) Mark off a $3\text{ ft} \times 2\text{ ft}$ space for the washbasin and a $2\text{ ft} \times 3\text{ ft}$ space for the toilet. Write the coordinates of the corners of these spaces.

Step 1 · Determine Coordinates for Washbasin and Toilet Spaces

Diagram 3

Washbasin space corners: $(-6, 0.5), \quad (-5, 0.5), \quad (-5, 2), \quad (-6, 2)$
Toilet space corners: $(-6, 3), \quad (-4.5, 3), \quad (-4.5, 4), \quad (-6, 4)$

Answer

(iii) Washbasin: $(-6, 0.5), (-5, 0.5), (-5, 2), (-6, 2)$ ; Toilet: $(-6, 3), (-4.5, 3), (-4.5, 4), (-6, 4)$

Common Mistakes

Swapping $x$ and $y$ coordinates: Writing points on the axes in reverse order, such as writing $(0, -6)$ instead of $(-6, 0)$ for point $\text{P}$ .
Sign Errors in the Second Quadrant: Forgetting that points to the left of the $y$ -axis have negative $x$ -coordinates (e.g., writing $(6, 9)$ instead of $(-6, 9)$ for point $\text{R}$ ).

Question 3

More questions in Exercise 1.2