Question

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.

Answer 1

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.