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Suppose that $A (5, 1)$ and $B (7, 5)$ be two points and $P$ be a point on $y = x$ such that $|P A - P B|$ is minimum then the point is $P$

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9,9

52,52

−195,0

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detailed solution

Correct option is B

Since the condition is |PA−PB| minimum, the point P lies on the line AB The equation of AB is y−5=5−17−5x−7y−5=2x−142x−y−9=0 Hence the point P is the point of intersection of the line 2x−y−9=0 and y=x Plug in y=x in the equation 2x−y−9=02x−x−9=0x=9 Therefore, the point P is P(9,9)

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