Homework Help

What is the difference between a coordinate geometry proof and a proof method that does...

user profile pic

ktchiate | Honors

Posted May 29, 2013 at 1:15 AM via web

dislike 1 like

What is the difference between a coordinate geometry proof and a proof method that does not use coordinates? When would it be ok to use a coordinate proof instead of another method?

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 29, 2013 at 2:38 AM (Answer #1)

dislike 1 like

A coordinate proof uses a coordinate system. This type of proof allows you to use algebraic techniques instead of only synthetic techniques. You can use coordinate proofs almost anytime that you could do a synthetic proof. Sometimes the algebra is "messy", and sometimes the algebra is too hard to do. Using coordinate geometry allows you to use equations of lines, the midpoint formula, the distance formula, equations for circles, ellipses, etc...

For example, you can prove the Pythagorean theorem using a coordinate proof: without loss of generality place the right angle of the triangle at the origin with the legs lying on the positive x and y axes. Let the vertex A be at (a,0), the vertex B be at (0,b) and the vertex C at (0,0) with `bar(AC)_|_bar(BC)` . Then by the distance formula

`AB=c=sqrt((a-0)^2+(0-b)^2)`

`==> c=sqrt(a^2+b^2)`

`==>c^2=a^2+b^2`

Care must be taken that you select an appropriate system.

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes