VCE Stuff > VCE Specialist Mathematics
VCE Specialist 3/4 Question Thread!
TrueTears:
let one side (adjacent to the right angle) be denoted by vector b, other side (the other side which is adjacent to the right angle) be denoted vector a, the hypotenuse is given by a-b, half of this vector is given by 1/2(a-b), from the right angle vertex to the midpoint; this vector is given by b+1/2(a-b) = 1/2(a+b)
compute the magnitude, the magnitude are also the same hence equidistant.
kamil9876:
TT, . Your attempt doesn't use the fact that it's a right angle triangle so that alerted me.
What you should now do is compute the length:
Likewise we can show that
Hence the magnitudes are indeed the same (notice this is false for certain triangles that are not right angled e.g: an iscosceles triangle with two very long equal sides and one very short side, this is a good way to check your proof, does it use all the assumptions?)
TrueTears:
--- Quote from: kamil9876 on December 06, 2011, 10:10:07 pm ---TT, . Your attempt doesn't use the fact that it's a right angle triangle so that alerted me.
What you should now do is compute the length:
Likewise we can show that
Hence the magnitudes are indeed the same (notice this is false for certain triangles that are not right angled e.g: an iscosceles triangle with two very long equal sides and one very short side, this is a good way to check your proof, does it use all the assumptions?)
--- End quote ---
thats right, i got lazy and didnt end up computing the lengths lol but yeah in my head using a.b = 0 was quite obvious from the start ;)
Bhootnike:
I don't get why the hypotenuse is a-b?
dc302:
--- Quote from: Bhootnike on December 06, 2011, 11:00:35 pm ---I don't get why the hypotenuse is a-b?
--- End quote ---
It's just a matter of 'how' you draw the triangle. I think the triangle is supposed to use the positive x, y axes, with the hypotenuse slanting down from the positive y axis to the positive x axis. Here I'm only saying x and y axes for illustrative purposes.
edit: actually a better visualisation: if vector b goes from origin to point B, and vector a goes from origin to point A, and AOB is the right angle, then the hypotenuse is from B to A, which is given by a-b. Draw it!
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