Answer:
9
Step-by-step explanation:
So first I created 2 distance forumlas and set them equal to each other
[tex]\sqrt{(5+1)^2+(k-2)^2} =\sqrt{(5-3)^2+(k)^2}[/tex]
then I simplified them
[tex](5+1)^2+(k-2)^2 =(5-3)^2+(k)^2\\[/tex]
[tex]36 + k^2 - 4k +4 = k^2 + 4[/tex]
[tex]-4k + 36 = 0\\[/tex]
[tex]4k = 36[/tex]
[tex]k = 9[/tex]
when k = 9, the two distances are equal
