Hello, I have an urgent question from a paper Watch

itsspelthannah
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https://www.google.co.uk/url?sa=t&rc...sS4NEQ2hGXN8l0

If anyone can read that link of an online copy I found, it is question 7.
From the pearson GCE mathematics advanced level a level unit 12 test.

I am completely stuck so any help is appreciated!
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old_teach
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I only taught Y8 maths, so this is likely to be wrong!
I worked out vectors of each line endpoint (eg M = 1/4 a)
Found out the midpoints of each line (added vectors and halved!)
Seemed to work - but I recommend you wait for someone who knows what they're doing!
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the bear
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if you can prove that KLNM is a parallelogram ( including a rectangle ) that is enough.
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Physikoi
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(Original post by itsspelthannah)
https://www.google.co.uk/url?sa=t&rc...sS4NEQ2hGXN8l0

If anyone can read that link of an online copy I found, it is question 7.
From the pearson GCE mathematics advanced level a level unit 12 test.

I am completely stuck so any help is appreciated!
Firstly, pick a common point that you can get to through both vectors (e.g. OP). Then express OP travelling through each diagonal individually.
e,g OP = OM + MP = OM + k(ML) and
OP = ON + NP = ON + z(NK)

where k and z are scalars. Basically, because you are proving they bisect each other, the scalars should be the same and equal to 0.5 .
Try and prove this using the above expressions
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