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# Reciprocal help?

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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...?

Apr 7, 2018

#1
+7350
+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?

Apr 7, 2018
edited by hectictar  Apr 7, 2018
edited by hectictar  Apr 7, 2018

#1
+7350
+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?

hectictar Apr 7, 2018
edited by hectictar  Apr 7, 2018
edited by 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? 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