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>

<p>this code generate a random point xy-plane named y0 then generate another point x0 10 steps apart from y0 in taxi distance .</p>

<p>------- begining of the code--------
   import random
   y0=(random.randint(0,50),random.randint(0,50))</p>

<pre><code>  while True:

      y=random.randint(0,50)

      x=(10 -abs(y-y0[1]))+y0[0] 
      if (abs(x-y0[0])+abs(y-y0[1]))==10:
         x0=(x,y)
         break
</code></pre>

python random