1. Nov 18, 2007

### STAR3URY

If L1 is perpendicular to L2, prove that the slope of L2 is the negative reciprocal of the slope of L1..

2. Nov 18, 2007

### EnumaElish

What is the definition of perpendicular? definition of slope? Any ideas?

3. Nov 18, 2007

### STAR3URY

Perpendicular is when two lines intersect to form 90 degree angles, slope is whether the line is moving up or down, and how much like the top value is the y and the bottom is the x.

4. Nov 18, 2007

### rock.freak667

If I tell you that the tangent of the angle that a line makes with any horizontal to it gives you the gradient. does that help?

5. Nov 18, 2007

### Dick

Draw the right triangle connecting the points (0,0), (x,0) and (x,y). Got it? So the hypotenuse has slope y/x. Now rotate it 90 degrees and tell me what the endpoint of that hypotenuse is? What's the slope of that hypotenuse?

6. Nov 18, 2007

### STAR3URY

My professor doesn't want us to use trigonometry cuz we didn't learn that yet..and Dick, im not sure im allowed to use that as a proof..

7. Nov 18, 2007

### Dick

If you can't rotate a point 90 degrees, then what's your definition of perpendicular?

8. Nov 18, 2007

### STAR3URY

During class all he told us was to prove that if
1). L1 is perpendicular to L2
2). slope of L1 is M1 where M1 can't be 0

prove that slope of L2 is -1/M1...thats it and he said not to use anything we didn't learn, he didnt talk about rotating anything, or trignometry. =(

9. Nov 18, 2007

### Dick

If you don't know that the line through the point (x,y) and (0,0) and the line through the point (-y,x) and (0,0) are perpendicular then I don't think we are going anywhere. What IS your definition of perpendicular?

10. Nov 18, 2007

### STAR3URY

Well i can't use my definition all he said was his definition, and thats that they intersect and the slope of l2 is negative recipricol and thats it...we have to prove that

11. Nov 18, 2007

### Dick

Oh, come on. You said the definition of perpendicular is that the lines meet at 90 degree angles. This means you can use some geometry. Use it.

12. Nov 19, 2007

### EnumaElish

Did you learn to define perpendicular in terms of inner products (of two vectors)?

13. Nov 20, 2007

### HallsofIvy

Staff Emeritus
That makes no sense. Apparently you want to PROVE that his definition is... what? Equivalent to some other definition, apparently! You can't PROVE that his definition is correct using only his definition! What is YOUR definition of perpendicular? That two lines intersect at 90 degrees?

14. Nov 20, 2007

In graph (orthonormal system) we know that if two lines are perpendicular then slope 1*slope 2 = -1 (it is a rule)
so slope 1 = -1/slope 2

15. Nov 21, 2007

### EnumaElish

One man's definition can be another's problem.

16. Nov 23, 2007