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Consider the points A (3, 4) and B (4, 13). If ‘P’ be a point on the line y = x such that PA + PB is minimum, then ‘P’ is. A) (13/7,13/7). B). (23/7,23/7) C) (31/7,31/7). D). (33/7,33/7)
Let P be the point as (x, x).then PA = root((x-3)^2 + (x-4)^2))and PB = root((x-4)^2 + (x-13)^2)PA + PB => root((x-3)^2 + (x-4)^2)) + root((x-4)^2 + (x-13)^2)Now to minimize it the whole expression should be equal to zero.that is (x-3)^2= 0 and (x-4)^2 = 0 and (x-13)^2 = 0Hence, x = 3 and x = 4 and x = 13Since only first option is the multiple of 13.it would be the answer. option.
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