How can I generate a random point (x, y) 10 steps apart from y0(a, b) in xy-plane?
<p>I have generated a random  point named <code>y0=(a,b)</code> in xy-plane , How can I generate another random point <code>(x,y)</code> 10 steps apart from <code>y0</code>? </p>

<p>note: by 10 steps apart from the firt point I don't mean the Euclidean distance. I mean the number of steps on lattice between the two point (a,b) and (x,y) which is given by |x-a|+|y-b|=10</p>

<p>My attempt(sometimes gives wrong result).</p>

<pre><code>import random
y0=(random.randint(0,50),random.randint(0,50))# here I generated the first point.
y=random.randint(0,50)

# I used the formula  |x-a|+|y-b|=10.
x=(10 -abs(y-y0[1]))+y0[0]  or x=-(10 -abs(y-y0[1]))+y0[0]

x0=(x,y)
</code></pre>

<pre><code>from random import random
from math import sqrt

# Deviation
dev = 50

# Required distance between points
l = 10

if __name__ == '__main__':

    # First random point
    x0, y0 = dev*random(), dev*random()

    # Second point
    x1 = dev*random()
    y1 = y0 + sqrt(l**2 - (x1 - x0)**2)

    # Output
    print "First point (%s, %s)" % (x0, y0)
    print "Second point (%s, %s)" % (x1, y1)
    print "Distance: %s" % (sqrt((x1 - x0)**2 + (y1 - y0)**2))
</code></pre>

python random