Thread: coordinate geometry-

The points have the following coordinates:
A(3,-2)
B(p,3)
C(6,2)
D(q,r)
The figure ABCD is a rhombus. Find the values of p, q and r.
Even though I used the midpoint formula and the distance formula, I could not deduce the values of p and q.
with the midpoint formula, i did get the value for r (-3).

Originally Posted by Ilsa

The points have the following coordinates:
A(3,-2)
B(p,3)
C(6,2)
D(q,r)
The figure ABCD is a rhombus. Find the values of p, q and r.
Even though I used the midpoint formula and the distance formula, I could not deduce the values of p and q.
with the midpoint formula, i did get the value for r (-3).

Hi Ilsa,

First find the slope of AC. That would be

Since the diagonals of a rhombus are perpendicular, the slope of BD would be

Next, find the midpoint of AC. That would be

Now, use points and slope to find the missing x-coordinate p.



This all boils down to

Since, M is also the midpoint of BD, we can easily find the coordinates of D this way:

and

Solving the above will yield and

The coordinates of the vertices of your rhombus are:

3, -2)" alt="A\3, -2)" />



6, 2)" alt="C\6, 2)" />



You can verify that ABCD is a rhombus by using the distance formula: