How do I find a random point on the hypotenuse?

I'm trudging through 5-6 years worth of forgotten math lessons and can't remember how to do this. I have a right triangle, the two sides both are equal to 30 so the angles are a clean 45 degrees a piece. I need to know how to determine the x,y coords of a random point on the hypotenuse. I have a diagram but forgive it's crudeness, it's just an example:

http://www.innerfilth.com/%7Emike/distance.gif

Those red dots are what I need to figure out. Ignore their position, since it's just an example. If I pointed to a random spot on that line, what math do I need to figure out the coords?

Hello, worldspawn!

The points are on the line: .$\displaystyle x + y \:=\:30\quad\Rightarrow\quad y \:=\:30- x$


So given an $\displaystyle x$-value, say, $\displaystyle x = 7$, then: .$\displaystyle y \:=\:30 - 7 \:=\:23$

Therefore, the point is: .$\displaystyle (7,\,23)$

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Originally Posted by worldspawn

I'm trudging through 5-6 years worth of forgotten math lessons and can't remember how to do this. I have a right triangle, the two sides both are equal to 30 so the angles are a clean 45 degrees a piece. I need to know how to determine the x,y coords of a random point on the hypotenuse. I have a diagram but forgive it's crudeness, it's just an example:

http://www.innerfilth.com/%7Emike/distance.gif

Those red dots are what I need to figure out. Ignore their position, since it's just an example. If I pointed to a random spot on that line, what math do I need to figure out the coords?

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You need to use Deep Blue.

Selecting any point on that line segment is a uniform distribution. We can model it this way: select a number uniformly in the interval [0,30]. Call it a, then the corresponding point on the line segment is (a,30-a).