Question 717966
Starting with Distance Formula, First take the square of distance between each point.


One variable assigning form can give like this:

D[1] (-1,2) to (-10,5), {{{D[1]^2=90}}}
D[2] (-1,2) to (-4,k), {{{D[2]^2=9+(2-k)^2}}}
D[3] (-10,5) to (-4,k), {{{D[3]^2=36+(5-k)^2}}}


Three equations using pythagorean theorem can be written for those distance squared expressions:

{{{D[1]^2=D[2]^2+D[3]^2}}}, 
and
{{{D[2]^2=D[1]^2+D[3]^2}}}, 
and
{{{D[3]^2=D[1]^2+D[2]^2}}}


Take the expressions for each and fill into the pythagorean theorem equations, and solve for k.  I did not finish the solution beyond what I wrote and posted so far.