slope formula : (y2 - y1) / (x2 - x1)
we will find the slope of side EF
(-3,5)...x1 = -3 and y1 = 5
(6,2)....x2 = 6 and y2 = 2
now we sub into the slope formula
slope = (2 - 5) / (6 - (-3) = -3 / (6 + 3) = -3/9 = - 1/3
so the slope of EF is 1/3
now we find the slope of GH
(4,-4)....x1 = 4 and y1 = -4
(-5,-1)..x2 = -5 and y2 = -1
now we sub into the slope formula
slope = (-1 - (-4) / (-5 - 4) = (-1 + 4) / -9 = -3/9 = - 1/3
so EF and GH are opposite sides...so opposite sides have the same slope because opposite sides of a rectangle are parallel...and congruent
now lets find the slope of FG
(6,2)...x1 = 6 and y1 = 2
(4,-4)..x2 = 4 and y2 = -4
sub into slope formula
slope = (-4 - 2) / (4 - 6) = -6/-2 = 3
and the slope of EH
(-3,5)....x1 = -3 and y1 = 5
(-5,-1)...x2 = -5 and y2 = -1
sub
slope = (-1 - 5) / (-5 - (-3) = -6 / (-5 + 3) = -6/-2 = 3
so EH and FG have the same slope...opposite sides are congruent
EF and FG are adjacent sides.....EF has a slope of -1/3 and FG has a slope of 3...so adjacent sides are perpendicular....because -1/3 and 3 are negative reciprocals. To find the negative reciprocal of a number, u flip the number and change the sign....so -1/3 (flip and change the sign) and 3/1 or just 3 are negative reciprocals and are perpendicular
In summary :
slopes of EF and GH are -1/3
slopes of FG and EH are 3
opposite sides are parallel and have the same slope
adjacent sides are perpendicular and have negative reciprocal slopes
