SOLUTION: Point A(1,4)is equidistant from the points (k,-2) and (4,k).find the value of K

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Question 723024: Point A(1,4)is equidistant from the
points (k,-2) and (4,k).find the value of
K
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Point A(1,4)is equidistant from the
points P(k,-2) and Q(4,k).find the value of
K
use the distance formula
d(AP) =sqrt%28%28k-1%29%5E2%2B%28-2-4%29%5E2%29
d(AQ) = sqrt%28%284-1%29%5E2%2B%28k-4%29%5E2%29
d(AP) = d(AQ)
sqrt%28%28k-1%29%5E2%2B%28-2-4%29%5E2%29 = sqrt%28%284-1%29%5E2%2B%28k-4%29%5E2%29
Take the square of both sides
%28%28k-1%29%5E2%2B%28-2-4%29%5E2%29 = %28%284-1%29%5E2%2B%28k-4%29%5E2%29

k%5E2-2k%2B1%2B36=9%2Bk%5E2-8k%2B16

simplify
6k=-12
k=-2