<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A point  $(x,y)$  in the first quadrant lies on a line with intercepts  $(a,0)$  and  $(0,b)$ , with  $a,b > 0$ . Rectangle  $M$  has vertices  $(0,0)$ ,  $(x,0)$ ,  $(x,y)$ , and  $(0,y)$ , while rectangle  $N$  has vertices  $(x,y)$ ,  $(x,b)$ ,  $(a,b)$ , and  $(a,y)$ . What is the ratio of the area of  $M$  to that of  $N$ ? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
1
A point  $(x,y)$  in the first quadrant lies on a line with intercepts  $(a,0)$  and  $(0,b)$ , with  $a,b > 0$ . Rectangle  $M$  has vertices  $(0,0)$ ,  $(x,0)$ ,  $(x,y)$ , and  $(0,y)$ , while rectangle  $N$  has vertices  $(x,y)$ ,  $(x,b)$ ,  $(a,b)$ , and  $(a,y)$ . What is the ratio of the area of  $M$  to that of  $N$ ?
test