specialist unit 2 vectors question!

[suskieanna]

Hello I am currently working on this topic and my sac is this week and I still haven't done my homework yet. It is just too difficult for me.. Somebody please help me with this question! This is from cambridge textbook. Because it is the proof part no answer for this question. The question is

8. Prove that the diagonals of a square are of equallength and bisect each other. I proved that the diagonals are of equal length but I don't know what to use (what property of a vector) to use to prove that both diagonals bisect

[S_R_K]

Hello I am currently working on this topic and my sac is this week and I still haven't done my homework yet. It is just too difficult for me.. Somebody please help me with this question! This is from cambridge textbook. Because it is the proof part no answer for this question. The question is

8. Prove that the diagonals of a square are of equallength and bisect each other. I proved that the diagonals are of equal length but I don't know what to use (what property of a vector) to use to prove that both diagonals bisect

In general, if you are finding the work difficult, talk to your teacher and seek help promptly. Your teacher is unlikely to be sympathetic if you seek last minute help when you had plenty of opportunity earlier on.

With respect to your question, suppose that we label the square's vertices as OABC. Then the diagonals are OB and AC. Let M be the midpoint of the diagonal OB, and let N be the midpoint of AC. OB and AC will bisect eachother if M = N. You can show that M = N by writing down the vectors OM and ON as some linear combination of vectors between the points O, A, B, C. Your aim is to show that OM and ON can be written as exactly the same linear combination of vectors. To do this, at some stage you'll need to use the fact that OABC is a square. Then, if OM = ON, we conclude that M = N, and hence OB and AC intersect at their midpoints.