Hi Ilsa,

First find the slope ofAC. That would be

Since the diagonals of a rhombus are perpendicular, the slope ofBDwould be

Next, find the midpoint ofAC. That would be

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

This all boils down to

Since,Mis also the midpoint ofBD, we can easily find the coordinates ofDthis 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 thatABCDis a rhombus by using the distance formula: