We know that the product of the slopes of two perpendicular lines is '-1' but.......?

Question

the slope of x-axis and y-axis is 0 and notdefined respectively.. They are perpendicular then their product is notdefined why this ambiquity?

Answer 1

The slope of any line is dy/dx. The x axis has no dy; i.e., dy=0 so dy/dx=0. The y axis has no dx; dx=0 so dy/dx = undefined.

Answer 2

Maybe this is off-topic, but why is it so many people here are saying that the slope of the y-axis is infinity? Couldn't it be just as likely negative infinity? As one tilts a line through the origin, the slope approaches positive infinity from one side, but negative infinity from the other.

That's why we say a vertical line has "no slope." Ganesh is correct when posing his question by saying the slope is not defined... but some of the answerers here need to understand that "undefined" is different than "infinity."

Answer 3

The slope of the x axis is 0 and the slope of the y axis is infinity. Rise over run. So the product of x and y is zero times infinity which is undefinable.

Answer 4

Hardy har har...


I remember asking one of the instructors at Cal, Berkeley a similar question.

I said "Does that mean that the product of zero and infinity is minus one"? He said, "No, you just have a special case there".

I might add that since you said that one is vertical and one is horizontal then we know that they are perpendicular because of how those are defined, so all is well!

Now that I'm a grad student in math maybe I can say something helpful.

This is another example of the problem with trying to divide by zero. You can use slang and say that a vertical wall has infinite slope but you can't do much math with it. In calculus you start to work effectively with the concept of infinity.

I think that it's good to ask such questions. But maybe it's just because I asked the same one many years ago!

Answer 5

Your statement is not true.

dy/dx= slope

X-Axises, by definition dy=zero

So dy/dx=0/dx=0 x 1/dx(any thing multiplied by 0=0)=0

Y-axis, by definition dx=0

So dy/dx=dy/0=dy x 1/0(1/0 is undetermined or undefined)

So one slope is zero and other slope is undefined.

So 0 x 1/0...Here 1/0 is undefined.

(any thing multiplied by 0=0)=0

So 0 x 1/0 = 0

So slopes of two perpendicular lines is 0 and not "-1"

QED

Answer 6

Hey there's no answer!
but i think something special
o * infinity is indeterminate
suppose it to be a square of an imaginary no
= i^2
= -1



is it ok

Answer 7

it is calculated utilising limits. enable the slope of a line be m1 and different be m2 perspective between them = Arc tan l (m1 - m2) / (a million + m1m2) l ?= Arc tan l m2(m1/m2 - a million) / m2(a million/m2 + m1) l ? = Arc tan l (m1/m2 - a million) / (a million/m2 + m1) l Taking the barriers, Lim m1 ?0 and m2?? m1/m2 ? 0 a million/m2 ? 0 We receive, ? = Arc tan l (0 - a million) / (0 + 0) l ? = Arc tan l-a million/0l ? = Arc tan ( ? ) = ?/2

Answer 8

slope i.e. tan is measured wrt x axis