Can you calculate the distance between two lines using a formula?

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Hey everyone,

Is there a formula for finding the distance between two slopes (sort of like a sideways trapezoid) ?
 
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Well, there's trigonometry.
 
Depends upon whether they are in Cartesian co-ordinates, or just the lengths are given (geometrical problem): so go with dick's in this case.

No, there is general formula (excluding cartesian).

And, you should not use "slopes" in this case (It would hurt later when you start calculus).
 
Ok thanks for the tips.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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