B. Example
Key Lesson Marker
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The slopes of vertical lines are not defined, so they become a special case when discussing slopes of perpendicular lines. Vertical and horizontal lines are perpendicular. |
A relationship you may have found in the Investigation is that
perpendicular lines have slopes that are
negative reciprocals. Another way of stating this relationship is that the slopes of perpendicular lines have a product of -1.
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Example 1 |
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Determine the slope of a line perpendicular to «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»y«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»5«/mn»«mo»)«/mo»«/math».
The slope of the given line is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mfrac mathcolor=¨#B94A48¨»«mn»3«/mn»«mn»4«/mn»«/mfrac»«/math». The negative reciprocal is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mfenced mathcolor=¨#B94A48¨»«mrow»«mo»-«/mo»«mfrac»«mn»4«/mn»«mn»3«/mn»«/mfrac»«/mrow»«/mfenced»«mo mathcolor=¨#B94A48¨»=«/mo»«mfrac mathcolor=¨#B94A48¨»«mn»4«/mn»«mn»3«/mn»«/mfrac»«/math»,
so the slope
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Recall that the reciprocal of a number can be found by swapping the numerator and denominator. A number that isn't expressed as a fraction has a denominator of 1.
For example, the number 2 can also be expressed as «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»1«/mn»«/mfrac»«/math». Therefore, the reciprocal of 2 is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math» and the negative reciprocal of 2 is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math».