Ex 1.2, 4

Transcript

Ex 1.2, 4 (i) Other rooms in the house: Reiaan’s room door leads from the dining room which has the length 18 ft and width 15 ft. The length of the dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners. Let’s draw this Given that Dining room has Length = 18ft, Width = 15ft The text says the length extends from P(−6, 0) to A (12, 0). Let's verify: 12−(−6)=18 feet. Now, Because the door into the bedroom is on this line, the dining room must sit below the bedroom on our graph (in the negative y -axis zone). If it goes down by 15 units, the new corners are: 𝑷(−𝟔,𝟎),𝐀(𝟏𝟐, 𝟎),(𝟏𝟐,−𝟏𝟓), and (−𝟔,−𝟏𝟓). Ex 1.2, 4 (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. First, find the center point of the dining room using the midpoint formula! X-midpoint X midpoint between -6 and 12 is: (−𝟔 + 𝟏𝟐)/𝟐=𝟑 Y-midpoint Y midpoint between 0 and -15 is: ((𝟎+(−𝟏𝟓)))/𝟐=−𝟕.𝟓 Thus, exact center of the room is (𝟑,−𝟕.𝟓). Next, center the 𝟓×𝟑 table over this point. The length (5ft) spans along the 𝑥-axis: So, its ends would be 3 + 2.5 = 5.5 3 – 2.5 = 0.5 The width (3ft) spans along the 𝑦-axis: So, its ends would be –7.5 + 1.5 = –(7.5 – 1.5) = –6 –7.5 – 1.5 = –(7.5 + 1.5) = –9 The coordinates of the table's feet are: (5.5, –6), (5.5, –9) (0.5, –6), (0.5, –9) Let’s mark in the figure