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

RMBS R(–4, 5), M(1, 4), B(2, –1), and S(–3, 0).

diagonals of a rhombus are perpendicular ... find slopes of the diagonals and show they're product is -1, which proves they are perpendicular.

slope of line RB = 6/-6 = -1
slope of line MS = 4/4 = 1

so -1 x 1 = -1 and that proves they are perpendicular and that the figure is a rhombus.
Hope that helps!! :)

Answer 2

@Mint_Blue_Rocks , do you think you could give a quick explanation on why -1 x 1 = -1 proves that they're perpendicular? I'm really awful with geometry..

Answer 3

Because of
slope of line RB = 6/-6 = -1
slope of line MS = 4/4 = 1
-1 and 1
You multiply -1 x 1 = -1
does that makes sense?