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Grade 11Analytical Geometry

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)

Profile image of Arapan Baranwal
9 Years agoGrade 11
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1 Answer

Profile image of Vikas TU
9 Years ago
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 = 0
Hence, x = 3 and x = 4 and x = 13
Since only first option is the multiple of 13.
it would be the answer.
  1. option.

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