Question 785281
The slope of the line containing the points (−7,1) and (−1,2) is
{{{(2-1)/(-1-(-7))=1/(-1+7)=1/6}}}
The slope of the line containing the points (3,k) and (−3,4) is
{{{(k-4)/(3-(-3))=(k-4)/(3+3)=(k-4)/6}}}
For two lines to be perpendicular, the product of their slopes must be {{{-1}}}.
{{{(1/6)*((k-4)/6)=-1}}}
{{{(k-4)/36=-1}}}
{{{k-4=-36}}}
{{{k=-36+4}}}
{{{highlight(k=-32)}}}
{{{drawing(300,300,-30,20,-40,10,
grid(0), red(line(-31,-3,23,6)),
green(line(5,-44,-4,10)),
green(circle(3,-32,0.5)),green(circle(-3,4,0.5)),
red(circle(-7,1,0.5)),red(circle(-1,2,0.5)),
red(circle(-7,1,0.3)),red(circle(-1,2,0.3))
)}}}