Question 894518: Prove that the points P (0, -4), Q (6,2), R (3,5) and S (-3, -1) are the vertices of a rectangle PQRS.
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 1) You could show opposites sides are equal length
2) You could show that angles are 90 degrees ie sides are perpendicular
3) You could show opposite sides are parallel.
I will show 2 and 3
P (0, -4), Q (6,2)
y= 1x-4 pq
, R (3,5) and S (-3, -1)
y= 1x+2 rs
pq and rs are parallel
r
s
q
p
y= -1x+8 r q
0, -4,-3, -1
y= -1x-4 p s
from the slope we can see that
pq and rs are parallel
rq and ps are parallel
pq and ps are perpendicular
rq and pq are perpendicular
rs and ps are perpendicular
rs and rq are perpendicular
we have two sets of parallel lines and 4 right angles
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