Chapter 1: Orienting Yourself: The Use of Coordinates
Chapter 1: Orienting Yourself: The Use of Coordinates
Exercise
Question
Question: 4 (ii)
9 / 9
9 / 9
Other rooms in the house:
(ii) Place a rectangular 5 ft × 3 ft dining table precisely in the centre of the dining room. Write down the coordinates of the feet of the table.
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Answer
1
Find the centre of the dining room using the coordinates of its corners.
Centre of the dining room and position of the dining table.
x-coordinate of centre = $\dfrac{(-6) + 12}{2} = 3$ $\quad$ ${color:#625b5f}[The dining room extends from x1 = -6 to x2 = 12]{/color}$
y-coordinate of centre = $\dfrac{0 + (-15)}{2} = -7.5$ $\quad$ ${color:#625b5f}[The dining room extends from y1 = 0 to y2 = -15]{/color}$
Therefore, the centre of the dining room is (3, -7.5).
2
Find the left and right x-coordinates of the table using its 5 ft side and the centre point.Note: The table is placed with its 5 ft side horizontally and its 3 ft side vertically.
\text{The 5 ft side is centred at x = 3, so the table extends $\dfrac{5}{2} = 2.5$ ft on either side of the centre.}
⇒ x1 = 3 - 2.5 = 0.5 and x2 = 3 + 2.5 = 5.5
So, the two x-coordinates of the table are 0.5 and 5.5.
3
Find the upper and lower y-coordinates of the table using its 3 ft side and the centre point.
\text{The 3 ft side is centred at y = -7.5, so the table extends $\dfrac{3}{2} = 1.5$ ft above and below the centre.}
⇒ y1 = -7.5 + 1.5 = -6 and y2 = -7.5 - 1.5 = -9
So, the two y-coordinates of the table are -6 and -9.
4
Combine the two x-coordinates and two y-coordinates to identify the four corners of the rectangular table.
Answer: The four corners of the table are: (0.5, -6), (5.5, -6), (5.5, -9), (0.5, -9).
Reason: Each corner is formed by combining one of the two x-coordinates with one of the two y-coordinates.
