Question

Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of M are M(3,-2). Find the slopes of sides KL, LM, NM, and NK.

Answer 1

For a rectangle the opposite sides are parallel, which means the slope of opposite sides will be the same.

So, 
Slope KL = Slope MN
Slope LM = Slope NK

Also two adjacent sides are perpendicular, so their slopes will be negative reciprocals of each other.

From the given points, we can find the slope of LM which will be:

$\frac{-2-(-4)}{3-1}= \frac{-2+4}{2} = 1$

So,

Slope of LM = 1
Slope of NK = 1

Slope of KL = Slope of NK = -1