Good afternoon Annela!

We use an “x-shift and y-shift” approach to do this question; this is essentially vectors.

In ABCD, vector AB = vector CD.

For example, if A to B is a shift 4 units rightwards and 8 units upwards, the same will be the case for D to C.

Alternatively, you can also use the fact that the diagonals of a parallelogram meet at a point which is the midpoint of both diagonals.

You can try this on your own first.

Let me know if you need me to do the working.

Can you show me the working using midpoint?

Can i ask why i cannot do like this (working is in green ink)?

Using lengths will be ok, but more tedious because square roots are involved. But in theory you should be getting the same answer as other methods.

The nice thing about parallelograms is that not only the lengths are equal. The directions are also equal! So their vector movement is identical, and hence we can use the easier method of midpoints or vectors rather than embark into the tougher length formula.

I will write this up at a later time when I have access to writing materials.

In your working, you cannot split the square root of a + b into square root a plus square root b.

Attempting the question via lengths.