if point A (1,4) is equidistant from points B(k,-2) and C(4,k), then find the value of k
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By distance formula,
Distance AB = Distance AC
( k - 1 ) ^2 + ( - 2 - 4 ) ^2 = ( 4 - 1 ) ^2 + ( k - 4) ^2
k^2 +1 - 2k + 36 = 9 + k^2 +16 - 8k
37 - 2k = 25 - 8k
-2k +8k = 25 - 37
6k = - 12
k = - 12 /6 = - 2
Distance AB = Distance AC
( k - 1 ) ^2 + ( - 2 - 4 ) ^2 = ( 4 - 1 ) ^2 + ( k - 4) ^2
k^2 +1 - 2k + 36 = 9 + k^2 +16 - 8k
37 - 2k = 25 - 8k
-2k +8k = 25 - 37
6k = - 12
k = - 12 /6 = - 2
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