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Okay, so I know the definition of a reciprocal is basically taking the quantity and dividing one with it.

However, it doesn't turn negative does it? In my text, it's asking to find the slop of a penperdicular line from the other slope. Using the slope given, I can use it to solve for the other slope.

 

Example:

\({n \over 2}\)\({2}\)

\({n \over 2}\)\({1 \over 2}\)

 

so n = 1... but the text states that the answer is -5. This answer is possible if \({1 \over 2}\) is negative, but I don't think it's possible...?

Guest Apr 7, 2018

Best Answer 

 #1
avatar+7153 
+3

The "reciprocal" of a number is just 1 divided by that number.

The reciprocal of   \(x\)   is   \(\frac1x\) .     The reciprocal of   \(\frac{a}{b}\)   is   \(\frac{b}{a}\) .

 

But the slopes of perpendicular lines are not just reciprocals of each other.

 

The slopes of perpendicular lines are negative reciprocals of each other. To find the slope of a line perpendicular to one with a given slope, we must take the negative reciprocal of the given slope. That means take the reciprocal of the slope and also multiply it by -1 .

 

For example...

 

If a line has a slope of  \(\frac34\) ,  the slope of a line perpendicuar  =  -\(\frac43\)

 

Take a look at this graph to see if the slope of the blue line is just  \(\frac43\) , it is not perpendicular to the red line, but if you change it to  -\(\frac43\) , then it is perpendicular:   http://www.desmos.com/calculator

 

I don't think I understand what your specific examples are.....Does this help though?

If not please don't hesitate to ask another question!  smiley

hectictar  Apr 7, 2018
edited by hectictar  Apr 7, 2018
edited by hectictar  Apr 7, 2018
 #1
avatar+7153 
+3
Best Answer

The "reciprocal" of a number is just 1 divided by that number.

The reciprocal of   \(x\)   is   \(\frac1x\) .     The reciprocal of   \(\frac{a}{b}\)   is   \(\frac{b}{a}\) .

 

But the slopes of perpendicular lines are not just reciprocals of each other.

 

The slopes of perpendicular lines are negative reciprocals of each other. To find the slope of a line perpendicular to one with a given slope, we must take the negative reciprocal of the given slope. That means take the reciprocal of the slope and also multiply it by -1 .

 

For example...

 

If a line has a slope of  \(\frac34\) ,  the slope of a line perpendicuar  =  -\(\frac43\)

 

Take a look at this graph to see if the slope of the blue line is just  \(\frac43\) , it is not perpendicular to the red line, but if you change it to  -\(\frac43\) , then it is perpendicular:   http://www.desmos.com/calculator

 

I don't think I understand what your specific examples are.....Does this help though?

If not please don't hesitate to ask another question!  smiley

hectictar  Apr 7, 2018
edited by hectictar  Apr 7, 2018
edited by hectictar  Apr 7, 2018
 #2
avatar
+1

You're explanation was very helpful! My apologies if my example wasn't very clear... I have another question that's similar to the example I did beforehand:

 

Given this pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?

 

\({3 \over n}\),\(-{7 \over 2}\)

 

If I cross multiply, the parallel slope is \(n = -{6 \over 7}\), is that right?

As for perpendicular... how would I solve for that?

Guest Apr 8, 2018

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