Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let A=(0,1) B=(0,0) C=(1,0)

Suppose that f(A) = (0.4,1.8), f(B) = (1,1), and f(C) = (1.8,1.6).

How do we prove that if its not a translate or glide, then its a rotation?

Is it because since glide is a combination of translation and reflection, and this if its not a translation and not a glide, then its also not a reflection. So it has to be a rotation?

share|improve this question
    
Are we assuming that $f$ is an isometry? –  Alex Becker May 15 at 5:50
    
Yes f is an isometry –  Instinct May 15 at 5:51
    
Are you asking for a proof that all isometries of the plane are of these forms, or a proof that this particular one is a rotation? –  Robert Israel May 15 at 6:44

1 Answer 1

You can tell (e.g. by computing the signed area of the triangle) that the transformation $f$ preserves orientation. This rules out reflections and glide reflections. And you can tell it's no translation since the line $AB$ intersects the line $f(A)f(B)$ in a finite point, so $AB\not\Vert f(A)f(B)$ therefore it's no translation either.

Illustration

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.