English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

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 ?

2007-09-06 07:02:41 · 7 answers · asked by sai kumar 1 in Science & Mathematics Mathematics

7 answers

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.

2007-09-06 07:07:37 · answer #1 · answered by Brian L 7 · 0 1

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

2007-09-06 13:40:43 · answer #2 · answered by chirpy 3 · 1 0

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

2016-12-16 13:07:21 · answer #3 · answered by Anonymous · 0 0

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

2007-09-06 07:17:09 · answer #4 · answered by mohanrao d 7 · 0 0

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.

2007-09-06 07:13:11 · answer #5 · answered by Amit Y 5 · 1 0

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

And gradient of the y-axis is infinity.

2007-09-07 11:16:34 · answer #6 · answered by Kemmy 6 · 0 0

It is -1 in the limit.

2007-09-06 19:45:41 · answer #7 · answered by Martin 5 · 0 0

fedest.com, questions and answers