Question 1106594
....


PQ
{{{y-2=((2-4)/(1-n))(x-1)}}}


{{{y-2=(-2/(1-n))(x-1)}}}


RS
{{{y-5=((5-3)/(1-4))(x-1)}}}

{{{y-5=-(2/3)(x-1)}}}




(a)
Lines to be parallel?
Slopes be equal.
{{{-2/(1-n)=-2/3}}}
Solve this for n.
-
{{{1/(1-n)=1/3}}}
{{{1-n=3}}}
{{{-n=3-1}}}
{{{highlight_green(n=-2)}}}



(b)
Lines to be perpendicular?
{{{-2/(1-n)=3/2}}}
Solve this for n.
-
cross-multiply,
{{{-4=3(1-n)}}}
{{{-4=3-3n}}}
{{{-4-3=-3n}}}
{{{3n=7}}}
{{{highlight_green(n=7/3)}}}