Coordinate Geometry

Question

The points A,B,C,D have coordinates (3,-2), B(p,3), C(6,2), D(q,r) respectively.The figure ABCD is a rhombus.Find

(a) the values of p,q,r

(b) the area of the rhombus

 

(a)P=1/2 q=8.5 r=-3

(b) 25 units^2

Answer 1

Hello David,

Let me outline the process:

1) For a Rhombus ABCD, AB=BC=CD=DA  using the distance formula you can get a simple equation that will get you a value of p. I have verified that p is 1/2.

2) using CD=AD gives you an equation with q & r as variables

3) Determine the slope of AC (4/3). For a Rhombus diagonal AC is perpendicular to BD so the slope of BD is (-3/4). This gives you another equation with q & r. Solve the simultaneous equations and you will have q & r.

4) Area of the rhombus is (1/2)(AC)(BD)

 

I believe in helping a student by pointing in the right direction and giving a "nudge". The rest is up to the student.

 

I hope this helps.

 

I am willing to tutor online.

 

Wishing you the best.

Pradip