The coordinates of the vertices of parallelogram rmbs are r(–4, 5), m(1, 4), b(2, –1), and s(–3, 0). using the diagonals, prove that rmbs is a rhombus. show all your work and state appropriate formulas and theorems used.

     x    y
R -4   5
M  1   4
B   2  -1
S  -3   0

Find the slope for opposite corners:
Slope = y2-y1 / x2 - x1

Opposite corners are:
R & B
M & S

-1 - 5 / 2 - (-4) = - 6 / 6 = -1
0 - 4 / -3 - 1 = -4/-4 = 1 

The slopes are reciprocal. They are identified as perpendicular lines because the slopes have opposite signs, one is positive 1 and the other is negative 1.

Perpendicular lines are lines that bisect at a right angle. One of the characteristics of a rhombus is that its diagonals bisect each other at a right angle. Thus, the given parallelogram is a rhombus.