Consider the point A≡(3,4) and B≡(7,13).If ′P′ be a point on line y=x such that PA+PB is minimum, then the coordinates of ′P′ is
A
(137,137)
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B
(237,237)
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C
(317,317)
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D
(337,337)
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Solution
The correct option is C(317,317) LetA′ is the reflection of A in y=x Image of any coordinate will get reversed in the mirror line y=x ⇒A1=(4,3) now PA+PB=A′P+PB which is minimum if A′,P,B are collinear. Equation of A1B is (y−3)=13−37−4(x−4)⇒3y=10x−31