Question

I need some help!!

Answer 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 2

To prove that RMBS is a rhombus, we need to state slopes of RM and BS, MB and SR are parallel to each other, and RM, BS, MB, and SR have the same distance(length).

Slope of RM: (4-5)/(1-(-4))=-1/5
Distance of RM: Use distance formula
d=sqrt((4-5)^2+(1-(-4))^2)=sqrt(26)

Slope of BS: (0-(-1))/(-3-2)=-1/5
Distance of BS: d=sqrt((-1-0)^2+(2-(-3))^2)=sqrt(26)

We just found that RM and BS have the same slope(means they are parallel to each other) and both lines are same length.

Use the same way to find the slope and distance of MB and SR.

Hope this will help.