# Help with line slope proof

• Mar 13th 2007, 01:49 PM
danb
Help with line slope proof
Hi, I am stuck on a geometry problem and it's really frustrating, it concerns the proof to the theorem that says "If two nonvertical lines are perpendicular, the product of their slopes is -1."

Now, this might be considered an algebra problem, but in the exercise I have to find the answer to:
http://img148.imageshack.us/img148/3...roblem1tk2.jpg
Please let me know if I need to include more information or anything if this seems vague, it's probably an easy problem but I just don't understand how to get the correct answer, thanks.
• Mar 13th 2007, 02:13 PM
Jhevon
Quote:

Originally Posted by danb
Hi, I am stuck on a geometry problem and it's really frustrating, it concerns the proof to the theorem that says "If two nonvertical lines are perpendicular, the product of their slopes is -1."

this is a wierd question, two lines are perpendicular when the product of their slopes are -1, period. doesn't matter if they are nonvertical or not. what tools do you have to use in this proof?

Quote:

Now, this might be considered an algebra problem, but in the exercise I have to find the answer to:
http://img148.imageshack.us/img148/3...roblem1tk2.jpg
Please let me know if I need to include more information or anything if this seems vague, it's probably an easy problem but I just don't understand how to get the correct answer, thanks.
ok, so we just do manipulations on the first equation so one side ends up looking like BD/DC, the other side should have some manipultions on m. here goes:

-DC/BD = m ...............BD/DC is positive, so make that side positive
=> DC/BD = -m ..........i just multiplied through by -1
=> BD/DC = -1/m ........i took the inverse, so now one side looks like what we wanted and the other side tells us what it is in terms of m
• Mar 14th 2007, 04:16 AM
topsquark
Quote:

Originally Posted by Jhevon
this is a wierd question, two lines are perpendicular when the product of their slopes are -1, period. doesn't matter if they are nonvertical or not.

I'm afraid it does. The "slope" of a vertical line is a/0 where a is some real number. The slope of a horizontal line is 0, but (a/0)*0 is undefined, not -1.

-Dan
• Mar 14th 2007, 06:59 AM
ThePerfectHacker
Quote:

Originally Posted by topsquark
I'm afraid it does. The "slope" of a vertical line is a/0 where a is some real number. The slope of a horizontal line is 0, but (a/0)*0 is undefined, not -1.

It seems to me you are getting more careful in mathematics. Is that true?
• Mar 14th 2007, 07:08 AM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
It seems to me you are getting more careful in mathematics. Is that true?

I know I'm getting more careful
• Mar 14th 2007, 07:13 AM
Jhevon
Quote:

Originally Posted by topsquark
I'm afraid it does. The "slope" of a vertical line is a/0 where a is some real number. The slope of a horizontal line is 0, but (a/0)*0 is undefined, not -1.

-Dan

so how would you prove that a vertical and a horiztontal line are perpendicular? represent the lines by vectors and using the dot product maybe? or use a line to connect two arbitrary points and show that the pythagorean theorem holds for the resulting triangle?
• Mar 14th 2007, 07:31 AM
ThePerfectHacker
Quote:

Originally Posted by Jhevon
so how would you prove that a vertical and a horiztontal line are perpendicular?

Theorem:Any two non-vertical lines are perpendicular if and only if the product of the slopes is -1.

Proof:Trivial.

Now, that theorem is true. Vertical lines do not apply to it.

Your question seems to be how can a vertical and horizontal line be parallel if they are not included in the theorem? But that no matter it one is talking about non-vertical lines.

You can show it like this.

Theorem:Let y=k be any vertical line, let x=j be any horizontal line. Then the two lines are perpendicular.

Proof:Line y=k is paralle with the x-axis (basically given). Line x=j is perpendicular with x-axis (they way you define rectangular coordinates are in terms of perpendicular and parallels so this and the statement before are basically given to us). Since x=j is perpendicular to a line parallel with y=k thus,
x=j is perpendicular with y=k.
Q.E.D.