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Let $A \equiv (3, - 4), B \equiv (1, 2) . Let P \equiv (2 k - 1, 2 k + 1)$ be a variable point such that PA+PB is the minimum. Then k is

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Correct option is C

We know that PA+PB≥AB (by triangle inequality). So, PA+PB is the minimum if PA+PB=AB, i.e., A,P,B are collinear. Therefore,3−411212k−12k+11=0or 3(2−2k−1)+4(1−2k+1)+1(2k+1−4k+2)=0or 3−6k+8−8k+3−2k=0or 14−16k=0∴k=78

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Let A≡(3,−4),B≡(1,2). Let P≡(2k−1,2k+1) be a variable point such that PA+PB is the minimum. Then k is

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Ready to Test Your Skills?

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Let $A \equiv (3, - 4), B \equiv (1, 2) . Let P \equiv (2 k - 1, 2 k + 1)$ be a variable point such that PA+PB is the minimum. Then k is