If product of slopes of 2 perpendicular lines is -1, Why is product of slopes of X and Y axes not= -1?

Question

If m1, m2 are slopes of two perpendicular lines, We know from cartesian geometry that their product m1.m2 = -1.
Even X and Y axes are perpendicular to each other.
why is it that the product of their slopes not equal to -1 ?

Answer 1

Two perpendicular slopes WON'T have a product equal to zero.

They'll have a QUOTIENT of -1.

Like this: One has a slope of 2, the other has a slope of negative 2.

Their product is -4.

Their QUOTIENT is -1.

As for why the X and Y axes don't do that? The Y axis has an undefined slope - it is a vertical line. Try to calculate the slope of a vertical line, and you have to divide by zero. The slope of the x axis is zero (not undefined, they're different), and you can't divide by zero there, either.

Answer 2

Hello Sai,
Of course you could try the limit approach - the slope of two perpendicular lines that get closer and closer to Y and X respectively. No matter how close they get to Y and X, the product of their slopes must still equal to -1. Therefore in the limit, the product of the slopes of Y and X must also equal to -1.

Another way to look at it is using the imaginary coordinate system. Here goes:
Y=iX
where i=imaginary operator, orthogonal to the real axis X, and by definition
i=squareroot of -1, therefore i*i=-1.

Also, you have X=-iY.

Transposing you get
Y=1/(-i)*X.

But 1/(-i)=i, therefore
Y=iX

(Because for any number a,
a/(-a)=-1.
It follows that i/(-i)=-1, which of course is equal to i*i. Therefore, 1/(-i) = i.)

So, the slope of both axes is i.

Then you get the product of the two slopes, which is i*i, which is, of course, -1....
chirpy

Answer 3

enable's get x-2y=7 interior the form of y = mx + b .... the place 'm' is the slope and 'b' is the y-intercept. ok........ x - 2y = 7 x - 7 = 2y x/2 - 7/2 = y ... or: y = a million/2x - 7/2 Now.... If the equation we are finding for is perpendicular to the only above, all of us understand that its slope is the *destructive reciprocal* of the slope of the equation above. So..... Slope of equation above = a million/2 *and* The destructive reciprocal of a million/2 is.... -2 so far, we've this lots to our new equation: y = -2x + b Now we can use those coordinates: (2, -4) x = 2 & y = -4 --------> -4 = -2(2) + b -4 = -4 + b 0 = b .......The Y-intercept = 0 Now we can write the equation...... y = -2x + 0 or.... y = -2x

Answer 4

slope of x - axis is 0
let slope of y - axis = m
m*0 = -1
m = -1/0 which is undefined
But other wise x and y axes are perpendicular

Answer 5

The slope of the X axis is zero. The slope of the Y axis is infinity.

0*infinity is undefined in the field of real numbers, and you have to use limits to calculate it.

Answer 6

Gradient of x-axis = 0
m1 x m2 = -1
m1 = -1/0
m1 = infinity

And gradient of the y-axis is infinity.

Answer 7

It is -1 in the limit.