As per the question,
Let the co-ordinate of the village A is (A, b) and the co-ordinate of the village B is (a, B)
Let the co-ordinate of the point of on the river is O, (x, 0)
As per the question, point A and B are lying on the straight line, so slop of AO and OB will be same,
the equation of line passing from the point (x, 0) and and (A, b)
Now substituting the values,
Now, taking the differenciation of both side with respect to,
for maxima and minima
, so distance will be minimum, if a=0 and b=0
Hence, will be the minimum distance.
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