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

#1**+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!

hectictar
Apr 7, 2018

#1**+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!

hectictar
Apr 7, 2018

#2**+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? W*

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

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