Question 785280
Slope of first pair, {{{(8-6)/(6-k)=2/(6-k)}}}.

Slope of second pair, {{{(-9-(-12))/(-7-0)=-3/7}}}


In order for the lines of each pair to be perpendicular, their slopes must be negative reciprocals of eachother:
{{{2/(6-k)=7/3}}}
{{{2=7(6-k)/3}}}
{{{6=7(6-k)}}}
{{{6=42-7k}}}
{{{7k=42-6}}}
{{{7k=36}}}
{{{k=36/7}}}


Your other two questions are handled similarly.