Question 723024
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((k-1)^2+(-2-4)^2)}}}

d(AQ) = {{{sqrt((4-1)^2+(k-4)^2)}}}

d(AP) = d(AQ)

{{{sqrt((k-1)^2+(-2-4)^2)}}} = {{{sqrt((4-1)^2+(k-4)^2)}}}

Take the square of both sides

{{{((k-1)^2+(-2-4)^2)}}} = {{{((4-1)^2+(k-4)^2)}}}


{{{k^2-2k+1+36=9+k^2-8k+16}}}


simplify
6k=-12
k=-2