Thats how I got the answers. I kinda used distance rule, but pythagorean theorem is the real answer to finding everything. I'm pretty sure that I'm correct.
Method:
You know from the fact that its a rhombus that each side is equal in length, and the opposite angles are equal. Since the rhombus is set on the x axis, and b is given as the y coordinate for the upper left vertice, the y coordinate for the upper right vertice also has to be b (its the height). That's solved just from the properties of it being a rhombus.
Okay, now, just from looking at the rhombus, you can tell that the length of the bottom side is a. However, do the distance formula to prove this (it's d1 in the image: d1= sqrt ( (a-0)^2 + (0-0)^2) = sqrt (a^2) = a). All of the sides are equal to a. Since the height is b, and the diagonal sides are a, make a small right triangle on the left side, a being the hypotenuse. Since a is the hypotenuse, and x^2 + y^2 = c^2, x and y being the triangle legs of a right triangle and c being the hypotenuse, we get x^2 + b^2 = a^2 --> x^2 = a^2 - b^2 --> x = sqrt ( a^2 - b^2 ). This is the x coord for the upper left vertices.
For the upper right vertices, the work is already done (we just did it). The x coord is the x we found PLUS a (its the smaller leg for the right triangle if you use that diagonal side as the hypotenuse).
I can make some more drawings if you need, as I know this isn't perfectly clear, but I'm pretty sure this is how you should find the answer.
