Explanation:

Use of comparative degree is incorrect here as we are not comparing the distance of two houses. We need superlative degree because we need to take shelter in the house which is at the shortest distance from us. Superlative adjectives are used to describe an object which is at the upper or lower limit of a quality (the tallest, the smallest, the fastest, the highest). Since, out of ‘n’ number of houses, we need to go inside the one which is at the shortest distance therefore we need to use the superlative degree. Thus option A is the correct choice.