Vectors Help!He

[dave101]

Hey guys,
I'm stuck on this vectors question from the new Cambridge spesh textbook from chapter 2 question 10 (a)

The question is .
ABCD is a trapezium with AB parallel to DC. X and Y are the midpoints of AD and BC respectively. (a) Express →XY in terms of a and b, where a = →AB and b = →DC.
Thanks in advance
 

[wyzard]

This is a tricky one, the trick here is to draw another line that is parallel to AD and shift it to the right, join up with C to create a triangle on the right side. See the attached image.

Now from the trapezium we see that (I'm dropping off the arrow signs for convenience) and since also , this means that .

As X and Y is the midpoint of AD and BC respectively, we can say that and , so .

So what is ? Now referring back to the trapezium, remember I said the trick was to draw another parallel line to AD to form a triangle on the right? then is just simply the vector , which is just because of its direction.

From here just substitute back into (replacing with ), obtaining

[dave101]

Wow! i would of never been able to think of that hahah.
Cheers, you are a true wyzard

[wyzard]

Wow! i would of never been able to think of that hahah.
Cheers, you are a true wyzard

Yeah took me a while to figure that out