# Thread: Help with line slope proof

1. ## 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:

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.

2. 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?

Now, this might be considered an algebra problem, but in the exercise I have to find the answer to:

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

3. 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

4. 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?

5. 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

6. 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?

7. 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.