Ok, so I recently came across this problem:
"Use slopes and distances to determine what kind of quadrilateral PQRS is created by each set of coordinate points.
$P(0,0), Q(0,2), R(5,5), S(2,0)$
$P(1,1), Q(5,1), R(4,8), S(2,8)$
$P(2,1), Q(7,1), R(7,7), S(2,5)$
$P(0,7), Q(4,8), R(5,2), S(1,1)$
$P(1,7), Q(5,9), R(8,3), S(4,1)$
$P(5,1), Q(9,6), R(5,11), S(1,6)$ "
I've tried all sorts of things involving slope and distance, but none are coming out or making any sense. Could some one please help me figure out what to do?
Hint:
(0) Sketch the points to get an initial guess. For example, #1 could be a kite.
(1) For equal distances -- if two pair of opposite sides are equal in length, that figure is a parallelogram (at least).
(2) For slopes --
(a) If $m_1 \times m_2 = -1$, we have two perpendicular lines.
(b) If two adjacent angles have the same characteristics of (a), it probably is a rectangle.
(c) If $m_1 = m_2$, then the two lines are parallel...