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coordianteｇｅｏｍｅｔｒｙ(下) 20分
圖片:http://uploadimage.org/images/x4oa9f2anjiecbbk1ipm.jpgin the fig. ab prepend. bc where c=(0,6) b=(4,8)1.find the coordinate of a2. find the length of ab and bc3. find the area of OABC.---------------Prove the st. line passing through A(2,3) and B(-4,-6) passes through the... 顯示更多 圖片:http://uploadimage.org/images/x4oa9f2anjiecbbk1ipm.jpg in the fig. ab prepend. bc where c=(0,6) b=(4,8) 1.find the coordinate of a 2. find the length of ab and bc 3. find the area of OABC. --------------- Prove the st. line passing through A(2,3) and B(-4,-6) passes through the origin ------------------------ open-ended How many st. lines are there on the Cartesian coordinate plane with slope 1? 最佳解答20分
最佳解答:
1. The coordinate of A is (a,0), since A is on the x-axis. AB is perpendicular to BC. (slope of AB) x (slope of BC) = -1 (0-8)/(a-4) x (8-6)/(4-0) = -1 4(a-4) = 16 Hence, a = 8 Ans: The coordinate of A is (8,0) ===== 2. AB = √[(8-4)2 + (0-8)2] AB = √(16 + 64) AB = √80 AB = 4√5 units BC = √[(4-0)2 + (8-6)2] BC = √(16 + 4) AB = 2√5 units ===== 3. Area of OABC = Area of ?ABC + Area of ?AOC Area of OABC = (1/2)xABxBC + (1/2)xAOxCO Area of OABC = (1/2)x(4√5)x(2√5) + (1/2)x8x6 Area of OABC = 20 + 24 Area of OABC = 44 sq.units ===== Prove the st. line passing through A(2,3) and B(-4,-6) passes through the origin The two-point form of the st. line passing through A and B is: (y-3)/(x-2) = (-6-3)/(-4-2) (y-3)/(x-2) = 3/2 2(y-3) = 3(x-2) 2y-6 = 3x-6 3x-2y=0 The line is (L): 3x - 2y = 0 Substitute (0,0) into (L): L.S. = 3(0) - 2(0) L.S. = 0 L.S. = R.S. Hence, the origin lies on the st. line. ===== How many st. lines are there on the Cartesian coordinate plane with slope 1? The point slope form of a st. line: y = mx + c Slope slope = 1 Hence, the formula of the st. line is y = x + c c is any real number. There are ∞ real numbers. Therefore, number of st. lines = ∞ =
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coordianteｇｅｏｍｅｔｒｙ(下) 20分
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發問:圖片:http://uploadimage.org/images/x4oa9f2anjiecbbk1ipm.jpgin the fig. ab prepend. bc where c=(0,6) b=(4,8)1.find the coordinate of a2. find the length of ab and bc3. find the area of OABC.---------------Prove the st. line passing through A(2,3) and B(-4,-6) passes through the... 顯示更多 圖片:http://uploadimage.org/images/x4oa9f2anjiecbbk1ipm.jpg in the fig. ab prepend. bc where c=(0,6) b=(4,8) 1.find the coordinate of a 2. find the length of ab and bc 3. find the area of OABC. --------------- Prove the st. line passing through A(2,3) and B(-4,-6) passes through the origin ------------------------ open-ended How many st. lines are there on the Cartesian coordinate plane with slope 1? 最佳解答20分
最佳解答:
1. The coordinate of A is (a,0), since A is on the x-axis. AB is perpendicular to BC. (slope of AB) x (slope of BC) = -1 (0-8)/(a-4) x (8-6)/(4-0) = -1 4(a-4) = 16 Hence, a = 8 Ans: The coordinate of A is (8,0) ===== 2. AB = √[(8-4)2 + (0-8)2] AB = √(16 + 64) AB = √80 AB = 4√5 units BC = √[(4-0)2 + (8-6)2] BC = √(16 + 4) AB = 2√5 units ===== 3. Area of OABC = Area of ?ABC + Area of ?AOC Area of OABC = (1/2)xABxBC + (1/2)xAOxCO Area of OABC = (1/2)x(4√5)x(2√5) + (1/2)x8x6 Area of OABC = 20 + 24 Area of OABC = 44 sq.units ===== Prove the st. line passing through A(2,3) and B(-4,-6) passes through the origin The two-point form of the st. line passing through A and B is: (y-3)/(x-2) = (-6-3)/(-4-2) (y-3)/(x-2) = 3/2 2(y-3) = 3(x-2) 2y-6 = 3x-6 3x-2y=0 The line is (L): 3x - 2y = 0 Substitute (0,0) into (L): L.S. = 3(0) - 2(0) L.S. = 0 L.S. = R.S. Hence, the origin lies on the st. line. ===== How many st. lines are there on the Cartesian coordinate plane with slope 1? The point slope form of a st. line: y = mx + c Slope slope = 1 Hence, the formula of the st. line is y = x + c c is any real number. There are ∞ real numbers. Therefore, number of st. lines = ∞ =
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