Question 1159130
given:

{{{L}}}({{{0}}},{{{4}}}), 
{{{M}}}({{{6}}},{{{ 0}}}), 
{{{N}}}({{{2}}}, {{{4}}})

to find: {{{O}}} ({{{x}}},{{{y}}})

first draw a picture:

{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(0,4,.12),locate(0.3,4,L(0,4)),
circle(6,0,.12),locate(6,-0.3,M(6,0)),
circle(2,4,.12),locate(2,4,N(2,4)),
green(line(0,4,2,4)),green(line(6,0,2,4)),
graph( 600, 600, -10, 10, -10, 10, 0)) }}}

since distance between {{{L}}}({{{0}}},{{{4}}}) and {{{N}}}({{{2}}}, {{{4}}}) is {{{2}}} units, and {{{LN=OM}}}, the distance between fourth vertice {{{O}}} and {{{M}}}({{{6}}},{{{ 0}}}) will be also {{{2}}} units to the left

if {{{M}}}({{{6}}},{{{ 0}}}) {{{2}}} units to the left will be at point ({{{4}}},{{{0}}})

so, fourth vertice is at ({{{4}}},{{{0}}})

put is on a graph

{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(0,4,.12),locate(0.3,4,L(0,4)),
circle(6,0,.12),locate(6,-0.3,M(6,0)),
circle(2,4,.12),locate(2,4,N(2,4)),
circle(4,0,.12),locate(4,-0.3,O(4,0)),
green(line(0,4,4,0)),green(line(4,0.1,6,0.1)),
green(line(0,4,2,4)),green(line(6,0,2,4)),
graph( 600, 600, -10, 10, -10, 10, 0)) }}}