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Question

Find the value of k, if the point P (0, 2) equidistant from (3, k) and (k , 5).

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Solution

P(0,2)
Q(3,k)
R(k,5)

PQ = square root of 3 squared plus left parenthesis k minus 2 right parenthesis squared end root
PR = square root of k squared plus left parenthesis 5 minus 2 right parenthesis squared end root
PQ =PR
square root of 3 squared plus left parenthesis k minus 2 right parenthesis squared end root=square root of k squared plus left parenthesis 5 minus 2 right parenthesis squared end root
9 plus left parenthesis k minus 2 right parenthesis squared equals k squared plus 9 k squared plus 4 minus 4 k minus k squared plus 9 minus 9 equals 0 4 minus 4 k equals 0 k equals 1
Hence k =1 for P to be equidistant from Q and R


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