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The gradient of a straight line segment (一条直线段的梯度).pdf

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The gradient of a straight line segment mc-TY-gradstlnseg-2009-1 In this unit we find the gradient of a straight line segment, and the relationships between the gradients of parallel lines and of perpendicular lines. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: • calculate the gradient of a line through two points; • use gradients to determine whether two lines are parallel; • use gradients to determine whether two lines are perpendicular. Contents 1. The gradient of a line 2 2. Parallel lines 5 3. Perpendicular lines 6 c www.mathcentre.ac.uk 1 mathcentre 2009 1. The gradient of a line The gradient of a line segment is a measure of how steep the line is. A line with a large gradient will be steep; a line with a small gradient will be relatively shallow; and a line with zero gradient will be horizontal. We can quantify this precisely as follows. Consider Figure 1 which shows three line segments. The line segment AD is steeper than the line segment AC . In turn, this is steeper than AB which is horizontal. We can quantify this steepness mathematically by measuring the relative changes in x and y as we move from the beginning to the end of the line segment. y
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