Provided that x1 = x2 and y1 = y2, the points p1 = (x1, y1) and p2 = (x2, y2) define a

Chapter 12, Problem 12.3.22

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Provided that x1 = x2 and y1 = y2, the points p1 = (x1, y1) and p2 = (x2, y2) define a rectangle with p1 in one corner and p2 in the opposite corner. We represent this rectangle as a 4-vector r = (x1, y1, x2, y2). For instance, Figure 12.27 shows the rectangle described by r = (2, 2, 7, 6), which has p1 = (2, 2) and p2 = (7, 6). (a) Sketch the rectangle described by s = (2, 4, 5, 8). 6T (b) Let t be a rectangle and let u = (1, 0, 1, 0), v = (0, 1, 0, 1), and w = u +v . Describe in words how the following rectangles are related to t . (i) t + u (ii) t + v (iii) t u (iv) t + 2u + 3v (v) t + w (vi) t +k w , k a constant. 2 7 2 6 p1 = (2