Ok, I appologise if this question is obvious, but I'm still a high school student. We all know that anything times 0 = 0.
We also know that to find out if two lines are perpendicular to one another their gradients multiply together to make -1. A horizontal line and a vertical one are perpendicular to one another. Their gradients are 0 and infinite. Therefore 0 x ∞ = -1 which contradicts the earlier rule. Is it that the "perpendicular lines gradients product is -1" rule is insufficient to accomodate this exception? Or is there some other explanation?
2006-07-24 13:54:38 · 5 answers · asked by The D 1 in Science & Mathematics ➔ Mathematics
If you look through the proof that the product of the gradients (slopes) is -1, you will see that it doesn't apply when one line is horizontal. However, in that case, the perpendicular line is clearly vertical.
2006-07-24 14:06:45 · answer #1 · answered by mathematician 7 · 1⤊ 0⤋
the rule is that x*0=0 when x is a number. Infinity is not a number, so the rule doesn't apply.
The gradients part:
a and b are perpendicular if grad(a)=-1/grad(b)
but if grad(b)=0, grad(a)=-1/0 which is ill-defined, as it is a division by zero.
This is always something to watch out for. You will always have a problem if you divide by zero.
Suppose x=2, and x=y
then x^2= xy
x^2-xy=0
x(x-y)=0
x=0=2
so 2=0
2006-07-25 11:24:03 · answer #2 · answered by hi_patia 4 · 0⤊ 0⤋
mathematican did not answer your question correctly. Look, the rule states that the product of the gradients is -1 given that the absolute value of one gradient is the reciprocal of the absolute value of the other gradient. |0| and |infinity| are not reciprocals of each other. This is the correct explanation. Infinity is undefined.
2006-07-24 22:13:37 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Just to get something straight here:
1/infinity = 0 and 1/0 = infinity.
THese are not indeterminate. They are accepted numbers.
Now to your question, go thru the proof for your -1 conclusion and you will see why it doesn't work in that particular instance.
2006-07-27 00:16:46 · answer #4 · answered by blind_chameleon 5 · 0⤊ 0⤋
the slope of the x axis is 0 and the slope of the y axis is 1/0 which is indeterminate
so the product of the slopes of x and y axes is never equal to –1.only if the slope
of any line is non zero-mind you-will the product of their slopes will be –1
2006-07-26 03:21:56 · answer #5 · answered by rumradrek 2 · 0⤊ 0⤋