Question 701328
first find the equation of the line passing through ({{{-5}}},{{{2}}}) and ({{{-2}}},{{{5}}})

*[invoke find_equation_of_line -5, 2, -2, 5]

than find the equation of the line passing through ({{{-5}}},{{{2}}}) and ({{{5}}},{{{-2}}})

*[invoke find_equation_of_line -5, 2, 5, -2]

than find the equation of the line passing through ({{{-2}}},{{{5}}}) and ({{{5}}},{{{-2}}})


*[invoke find_equation_of_line -2, 5, 5, -2]


now graph all three lines together:

{{{y=x +7}}}.........a slope is {{{m=1}}}

{{{y=-0.4x }}}.........a slope is {{{m[1]=-0.41}}}


{{{y=-x + 3}}}.........a slope is {{{m[2]=-1}}} which is negative reciprocal of {{{m=1}}}; {{{m[2]=-1/m=-1/1=-1}}}...so, the line {{{y=x +7}}} and {{{y=-x + 3}}} are perpendicular to each other

if two of lines perpendicular to each other, and three intersecting line form a triangle, triangle is a right angle triangle
 


{{{drawing( 600, 600, -10,10, -10, 10,locate(-2.5,4.5,"90°"), graph( 600, 600, -10,10, -10, 10, x + 7, -0.4x,-1x + 3 )) }}}