prove that perpendicular lines have opposite and reciprocal slopes.
i just want to know how. to see if i can resolve a question...

Question

lilcathyx · Answer

i do that by using the slope formula ?  the m= $$y2-y1 \over x2-x1$$

lilcathyx · Answer

@haleyelizabeth2017  what do you think ?

lilcathyx · Answer

@phi  ?

phi · Answer

I'll have to think about it.  we need an idea.

lilcathyx · Answer

mhmmm.. okkay. an idea.. im sorry i dont understand this a lot.

lilcathyx · Answer

this is the question " Triangle QRS has been rotated 90° to create triangle TUV. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes. You must show all of your work to receive credit.
"

lilcathyx · Answer

90 degrees to create*

phi · Answer

can you post a screen shot of the picture ?

lilcathyx · Answer

attachment

lilcathyx · Answer

Yep ;o

phi · Answer

Did you make that graph or was it given.  I only ask, because the triangles are also reflected... not quite what you want.

lilcathyx · Answer

That is the graph that was given

phi · Answer

they claim the two lines SR and UV
form 90 deg angle.  

ok, let's find the slope of line SR  
and the slope of UV
and see if we get  negative reciprocals

lilcathyx · Answer

SR = 3/3 = 1   & UV = -3/3 = -1

lilcathyx · Answer

aren't they opposite reciprocals ?

lilcathyx · Answer

i don' think they are negative reciprocals..

phi · Answer

1 is special.  If we got 2  and - 1 /2  it would be obvious.
but with 1, we do have negative reciprocals.  But to see it, write it like this:
$$ -1 = \frac{1}{-1} $$
now you have $ 1  \text{ and } \frac{1}{-1} $
which are negative reciprocals.

so you have shown the 90 degree lines have negative reciprocals

phi · Answer

Apparently  people have introduced "opposite reciprocal" as a new way to say
negative reciprocal.   (who knows why ?!).  But they mean the same thing:
$ a \text{ and } -\frac{1}{a} $
when you multiply them you get -1.

lilcathyx · Answer

That is all i have to do to prove that perpendicular lines have opposite and reciprocal slopes ?

phi · Answer

I think that is what they want for this problem.  But we have not proved that *all* perpendicular lines have opposite reciprocals,  only the pair of lines in this problem.

Proving it's true all the time is harder... a lot harder... so I don't think that is what they want.

lilcathyx · Answer

Oooohh i see. Thank you for helping phi :) ^.^