Question 1177583
Triangles {{{ABC}}} and {{{DEF}}} are shown. 

{{{A}}} ({{{4}}}, {{{2}}}) 
{{{B }}}({{{4}}}, {{{5}}})
{{{C}}} ({{{1}}}, {{{2}}})  

{{{D}}} ({{{2}}}, {{{-4}}}) 
{{{E}}}({{{5}}}, {{{-4}}})
{{{F}}} ({{{2}}}, {{{-1}}}) 

Line {{{BC}}} and line {{{EF}}} intersect at point ({{{0}}}, {{{1}}})

Line {{{BC}}},{{{ y=mx+b}}},  passes through {{{B }}}({{{4}}}, {{{5}}})  and {{{C}}} ({{{1}}}, {{{2}}}) 

use them to find slope {{{m}}}

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m=(2-5)/(1-4)}}}
{{{m=-3/-3}}}
{{{m=1}}}

so far
{{{ y=x+b}}}

 line {{{EF}}},{{{ y=mx+b}}},   passes through  {{{E}}}({{{5}}}, {{{-4}}})  and {{{F}}} ({{{2}}}, {{{-1}}}) 

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}
{{{m=(-1-(-4))/(2-5)}}}
{{{m=3/-3}}}
{{{m=-1}}}

{{{ y=-x+b}}}

Line {{{BC}}} and line {{{EF}}} intersect at point ({{{0}}}, {{{1}}})=>{{{b=1}}}

Line {{{BC}}} is  {{{ y=x+1}}}
line {{{EF}}}  is  {{{ y=-x+1}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(4,2,.12), locate(4,2,A),
circle(4,5,.12), locate(4,5,B),
circle(1,2,.12), locate(1,2,C),
line(4,2,4,5),line(4,2,1,2),line(1,2,4,5),

circle(2,-4,.12), locate(2,-4,D),
circle(5,-4,.12), locate(5,-4,E),
circle(2,-1,.12), locate(2,-1,F),
green(line(2,-4,5,-4)),green(line(2,-4,2,-1)),green(line(2,-1,5,-4)),
graph( 600, 600, -10, 10, -10, 10, x+1, -x+1)) }}}