If the point p (k-1,2)is equidistant from the point A (3, k) and B(k, 5),find the value of K.

If the point p (k-1,2)is equidistant from the point A (3, k) and B(k,

1.	If the point p (k-1,2)is equidistant from the point A (3, k) and B(k, 5),find the value of K.
Answer» We know that\xa0{tex}P A = \\sqrt { ( k - 1 - 3 ) ^ { 2 } + ( 2 - k ) ^ { 2 } }{/tex}and{tex}P B = \\sqrt { ( k - 1 - k ) ^ { 2 } + ( 2 - 5 ) ^ { 2 } }{/tex}Given that PA = PBSquaring both the sides,PA2 = PB2{tex}\\Rightarrow{/tex}\xa0(k - 1 - 3)2 + (2 - k)2 = (k - 1 - k)2 + (2 - 5 )2{tex}\\Rightarrow{/tex}\xa0(k - 4)2 + (2 - k)2 = (-1)2 + (3)2{tex}\\Rightarrow{/tex}\xa0k2 + 16 - 8k + 4 + k2 - 4k = 1 + 9{tex}\\Rightarrow{/tex}\xa02k2 - 12k + 10 = 0{tex}\\Rightarrow{/tex}\xa0k2 - 6k + 5 = 0{tex}\\Rightarrow{/tex}\xa0k2 - 5k - k + 5 = 0{tex}\\Rightarrow{/tex}\xa0k(k - 5) -1(k - 5)= 0{tex}\\Rightarrow{/tex}\xa0(k - 5)(k - 1) = 0{tex}\\Rightarrow{/tex}\xa0k = 5 or k = 1