Question

1. 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

First, plot the points. Point R would be somewhere in the second Quadrant, point M would be in the first quadrant 1, point B would be in the fourth quadrant, and point S would be on the negative y-axis. A property of rhombi is that their diagonals are perpendicular. One would need to calculate the slopes of the diagonals and determine whether or not they are perpendicular. Lines are perpendicular if and only if their slopes are opposite reciprocals. Example: 2 and -0.5
Formulas needed:
Slope formula:
$\frac{ y_{2}- y_{1} }{ x_{2} - x_{1} }$

The figure would look kinda like this:
      R
                  M
  
          S
                       B
 Diagonals are segment RB and segment SM
So, your slope equations would look like this:
 $\frac{-1-5}{2-(-4)}$
and
$\frac{4-(-3)}{1-0}$
Slope of RB= -1
Slope of SM=7
Not a rhombus, slopes aren't perpendicular. But this figure may very well be a parallelogram