The question is unclear but I read the 4 points as: A (0, 6), B (4, 1), C (-4, 0), D (-8, 7).
Those 4 points, ABCD do form a convex quadrilateral.
But the 2 pairs of opposite sides are then not parallel, so it's not a rhombus!
Here's how to tackle. it.
(a) Find the slope of AB, using (yB - yA)/(xB - xA). Do the same for CD. The 2 slopes should be equal, meaning AB || CD.
Do the same for AD and BC. They should also have the same slopes , so AD || BC.
Therefore, ABCD is a parallelogram.
To be a rhombus (a squashed over square), the 4 sides must also be equal in length.
Use the distance formula L = √((x12 - x22) + (y12 - y22)) to calculate the lengths of the above pairs of sides. They should all be equal => ABCD is a rhombus.
(b) To show that the diagonals, AC and BD, are perpendicular, calculate their slopes. mAC and mBD.
If mAC x mBD = -1, then AC is ⊥ BD
Calculate mAC and mBD by (yC - yA) / (xC - xA) and (yB - yA / (xB - xD)
Check that mAC x mBD = -1 which proves that AC ⊥ BD, as required.