Question

Discuss the differences between a coordinate geometry proof and a proof method that does not require coordinate geometry. When would it be appropriate to use a coordinate proof rather than another proof method?

Answer 1

oh god.

Answer 2

Just something simple and quick is fine.

Answer 3

hold on I'm not sure how to do this. I've only done this once before

Answer 4

I'll find a tutorial or something

Answer 5

Alright .

Answer 6

If you had some universal property that could be described by co-ordinates universally, then a co-ordinate proof would be in order. These are often used for circle center proofs, and for mid points of triangles or quadrilaterals..

If you cannot express the property you are trying to prove, or use, easily as co-ordinates , then use a paragraph, or two column proof, or statement-reason proof. A difficult idea to express with co-ordinates would be the 90° angle on a circle inscribed diameter. Not impossible to do…. just tedious and longer.
( you would need the slope of each line, to the ends of the diameter points, the perp formula,m1 m2 = -1 and the fact that the top points (x,y) must always lie ON the circle )

Eg of a co-ordinate proof outline :
Suppose you had a general triangle ABC, with vertices of (a1,a2) (b1,b2) , (c1,c2)

then the midpoints of the two sides would always be :
((a1+b1) /2 , (a2 +b2)/2) and ((c1 +b1)/2 , (c2+b2)/2)

and you could use these general points to prove the triangle " Side Splitter " theorem , or to show that the midpoint is always parallel to the base segment, or to prove that the mid point line has length of half the base.

I think in general I could prove these three items , much faster using similar triangles, and a statement – reason proof…. but this co-ordinate proof would also work .

Answer 7

Thank you!!

Answer 8

lol its loooong