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Course: MATH 1010, Fall 2011
School: UOIT
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DISCUSSION GROUP QUESTIONS Page 26 1. a. Let P1 = (2,6) and P2 = (4,3). Then we have x1 = 2, y1 = 6, x2 = 4, and y2 = 3. Using formula (1), we have d = ( -4 - 2) 2 + (3 - 6) 2 = 36 + 9 = 45 = 3 5 as obtained in Example 1. b. Let P1(x1,y1) and P2(x2,y2) be any two points in the plane. Then the result follows from the equality ( x2 - x1 ) 2 + ( y2 - y1 ) 2 = ( x1 - x2 ) 2 + ( y1 - y2 ) 2 . Page 27 1. a. All points...

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DISCUSSION GROUP QUESTIONS Page 26 1. a. Let P1 = (2,6) and P2 = (4,3). Then we have x1 = 2, y1 = 6, x2 = 4, and y2 = 3. Using formula (1), we have d = ( -4 - 2) 2 + (3 - 6) 2 = 36 + 9 = 45 = 3 5 as obtained in Example 1. b. Let P1(x1,y1) and P2(x2,y2) be any two points in the plane. Then the result follows from the equality ( x2 - x1 ) 2 + ( y2 - y1 ) 2 = ( x1 - x2 ) 2 + ( y1 - y2 ) 2 . Page 27 1. a. All points on and inside the circle with center (h, k) and radius r. b. All points inside the circle with center (h, k) and radius r. c. All points on and outside the cricle with center (h, k) and radius r. d. All points outside the circle with center (h, k) and radius r. 2. a. y 2 = 4 - x 2 and so y = 4 - x 2 b. (i) The upper semicircle with center at the origin and radius 2. (ii) The lower semicircle with center at the origin and radius 2. Page 28 1. a. Let P(x,y) be any point in the plane. Draw a line through P parallel to the y-axis and a line through P parallel to the x-axis (see figure). The x-coordinate of P is the number corresponding to the point on the x-axis at which the line through P hits the x-axis. Similarly y is the number that corresponds to the point on the y-axis at which the line parallel to the x-axis crosses the y-axis. To show the converse, reverse the process. b. You can use the Pythagorean Theorem in the Cartesian Coordinate System . This simplifies the computations greatly. 1 Preliminaries 48 Page 34 1. Refer to the accompanying figure. Observe that triangles P1Q1P2 and P3Q2P4 y - y1 y4 - y3 . Since P3 and P4 are are similar. From this we conclude that m = 2 = x2 - x1 x4 - x3 arbitrary, the conclusion follows. Page 37 1. a. We obtain a family of parallel each lines having slope m. b. We obtain a family of straight lines all of which pass through the point (0,b). Page 40 1. In Example 11, we are told that the object is expected to appreciate in value at a given rate for the next five years, and the equation obtained in that example is based on this fact. Thus, the equation may not be used to predict the value of the objectvery much beyond five years from the date of purchase. 49 1 Preliminaries EXPLORING WITH TECHNOLOGY QUESTIONS Page 38 1. The straight lines L1 and L2 are shown in the figure that follows. 2. a. L1 and L2 seem to be parallel to each other. b. Writing each equation in the slope-intercept form gives 41 y = -2 x + 5 and y = - 20 x + 11 . 20 from which we see that the slopes of L1 and L2 are 2 and 14/20 = 2.1, respectively. This shows that L1 and L2 are not parallel to each other. The straight lines L1 and L2 are shown in the following figure. a. L1 and L2 seem to be perpendicular to each other. b. The slopes of L1 and L2 are m1 = 1/2 and m2 = 5, respectively. 1 1 1 , we see that L1 and L2 are not perpendicular to each Since m1 = - - = - m2 2 5 other. Page 39 1. The straight lines with the given equations are shown in the figure that follows. 1 Preliminaries 50 Changing the value of m in the equation y = mx + b changes the slope of the line and thus rotates it. 2. The straight lines of interest are shown in the following figure. Changing the value of b in the equation y = mx + b changes the y-intercept of the line and thus translates it (upwards if b > 0 and downwards if b < 0). 3. Changing both m and b in the equation y = mx + b rotates as well as translates the line. 51 1 Preliminaries
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Washington - CHEM 162 - 162
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Washington - CHEM 162 - 162
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Washington - CHEM 162 - 162
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Washington - PHYS - 115
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Washington - PHYS - 115
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