The Student Room Group

Product of gradient of perpendicular lines

I know that if we multiply the gradient of 2 perpendicular lines they must be equal to -1. But why doesn't it applies when the lines are the x-axis(y=0) and the y-axis(x=0)..

The gradient of the x-axis will be 0(zero).
The gradient of the y-axis will be \infty .

So the product will be, 0×1 0 \times \infty \not= -1 .

Can any body please tell me why this happen.

Thanks in advance
Reply 1
The gradient of the y-axis is not \infty

As lines tend towards the y-axis their gradient tends towards infinity
Reply 2
Original post by TenOfThem
The gradient of the y-axis is not \infty

As lines tend towards the y-axis their gradient tends towards infinity


So the gradient of the y-axis is not infinity?

dydx=dy0= \dfrac{dy}{dx} = \dfrac{dy}{0} = \infty

I cannot understand the mistake.
Reply 3
division by 0 is undefined and does not ==\infty
Reply 4
the working for it would be better like this

x=nx = n


dxdy=0\dfrac{dx}{dy} = 0


dydx=10\dfrac{dy}{dx} = \dfrac{1}{0}


but it still does not give \infty
Reply 5
Original post by TenOfThem
the working for it would be better like this

x=nx = n


dxdy=0\dfrac{dx}{dy} = 0


dydx=10\dfrac{dy}{dx} = \dfrac{1}{0}


but it still does not give \infty


So how should i find the product of gradient of these two lines?

I understand that division by zero is undefined and the gradient is not infinity but it tends towards infinity.
Reply 6
Why do you need to find the gradient product?

You know that if one line is x=a and you want a line perpendicular it will be y=b
Reply 7
Original post by TenOfThem
Why do you need to find the gradient product?

You know that if one line is x=a and you want a line perpendicular it will be y=b


I just want to know why the normal method(gradient of 2 perpendicular lines equals -1) doesn't work here.
Reply 8
Just because one of the gradients is undefined
Reply 9
Original post by TenOfThem
Just because one of the gradients is undefined


Is their any detailed explanation of it?

Does it mean that the method, gradient of two perpendicular lines equals -1, is not always true, right?
Where the gradient of both lines is defined the rule holds true

division by 0 always creates a problem

There may be a more detailed explanation that I am unaware of
Reply 11
Original post by TenOfThem
Where the gradient of both lines is defined the rule holds true

division by 0 always creates a problem

There may be a more detailed explanation that I am unaware of


Thanks for your help. I will inform you if i get more detailed explanation about it.

Quick Reply

Latest