Question 1155397
 

given:

L({{{0}}},{{{4}}}), -> lie on horizontal line-{{{y=4}}}
 M({{{6}}}, {{{0}}}), -> lie on vertical line-{{{x=6}}}
N({{{2}}}, {{{4}}}) -> lie on horizontal line-{{{y=4}}}, two units to the right from {{{L}}}

if a parallelogram {{{LMNP}}}, opposite sides are parallel and congruent: so,

{{{LN || PM}}} and {{{LN=PM}}}
distance from L to N is {{{2}}} units
=> distance from P to M is {{{2}}} units

since the line that contains {{{L}}} and {{{P}}} is parallel to the line that contains {{{M}}} and {{{N}}}, point {{{P}}} must be {{{2}}} units left  from the point {{{M}}}

so, the possible coordinates for the fourth vertex are: 
 {{{P}}}({{{4}}}, {{{0}}})




{{{drawing( 600, 600, -10, 10, -10, 10,

circle(0,4,.12), locate(0.3,4.5,L),
circle(6,0,.12), locate(6,-0.5,M),
circle(2,4,.12), locate(2,4.5,N),
circle(4,0,.12), locate(4,-0.5,P),
line(0,4,2,4), line(0,4,4,0),
line(6,0,2,4), line(6,0,4,0),

 graph( 600, 600, -10, 10, -10, 10, 0)) }}}