Can someone please talk me through this question?

I've been given this question as homework, but have never had a lesson on it and don't know what it means. Would anyone be willing to "walk me through" it?

For simplicity's sake let's just say every capital letter I use is a vector (e.g. AB = AB vector);



24a) First thing you need to know about vectors is that OA+AB= OB (random example). If you have a common middle point (A), then adding the two together will get you the value of one point to another (O to B)
OA refers to how far A is from point O = OP+PA = OA = a + a = 2a
Thus, OA = 2a.
If you're trying to find AB, you're not given any data on the right side of the triangle, so you'll have to use AO + OB.
Second thing you need to know about vectors is that when you flip OA to AO, all you need to do is add a negative sign to the value.
So OA = 2a. AO = -2a.
OB is given as 2b, hence,
AB = AO + OB = -2a + 2b = 2b - 2a

b) PQ = PA + AQ
PA is a (given)
AQ is given as 1/4 AB = 1/4(2b-2a)
PQ = a+ 1/4(2b-2a) = a + 1/b - 1/a = 1/2 a + 1/2 b
I don't really understand how much more you can explain it other than PQ = PA + AQ, sorry, so maybe someone else can help you with that.

c) Note that M is the middle point (given in question), hence AM = 1/2AB = (2b - 2a)/2 = b - a
OM = OA + AM = 2a + b - a = a + b

d) I'm not really sure about this, but from what I recall, the reason why b and c show that the shape is a trapezium is because PQ (given in (b)) and OM (given in (c)) are factors of each other (one is 1/2 of the other) which shows they are parallel, and that is a characteristic of a trapezium.

Hope this helps clarify some things. I'm not the best at math, so I can't go into full detail with explanations and someone will probably do it better, but I tried my best. Hope you get more replies. Best wishes.