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
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answer #1
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answered by Brian L 7
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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
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answer #2
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answered by chirpy 3
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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
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answer #3
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answered by Anonymous
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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
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answer #4
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answered by mohanrao d 7
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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
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answer #5
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answered by Amit Y 5
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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
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answer #6
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answered by Kemmy 6
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It is -1 in the limit.
2007-09-06 19:45:41
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answer #7
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answered by Martin 5
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