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Question

If the point P(k1,2) is equidistant from the points A(3,k) and B(k,5), find the values of k.

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Solution

Point P (k1,2) is equidistant from the points A(3,k) and B(k,5).
PA=PB or PA2=PB2
(3k+1)2+(k2)2=(kk+1)2+(52)2
(4k)2+(k2)2=12+32
168k+k2+k24k+4=1+9
2k212k+20=10
2k212k+2010=0
2k212k+10=0
k26k+5=0
k2k5k+5=0
k(k1)5(k1)=0
(k5)(k1)=0
k=1 or k=5.

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